Ovide Arino: Friend and maestro 24th April 1947–29th September 2003

Eva Sánchez

doi:10.1016/j.crvi.2004.09.010

Ovide Arino: Friend and maestro 24th April 1947–29th September 2003

Eva Sánchez ¹

¹ Dpto. Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, Spain

Comptes Rendus. Biologies, Volume 327 (2004) no. 11, pp. 955-960.

Métadonnées

Publié le : 2004-11-01

DOI : 10.1016/j.crvi.2004.09.010

Affiliations des auteurs :

Eva Sánchez ¹

¹ Dpto. Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, Spain

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Eva Sánchez. Ovide Arino: Friend and maestro 24th April 1947–29th September 2003. Comptes Rendus. Biologies, Volume 327 (2004) no. 11, pp. 955-960. doi : 10.1016/j.crvi.2004.09.010. https://comptes-rendus.academie-sciences.fr/biologies/articles/10.1016/j.crvi.2004.09.010/

Version originale du texte intégral

Ovide Arino¹ was born in Toulouse (France) on 24th April 1947. He studied mathematics at the University of Nice (France), where his professors included high-profile French mathematicians such as Dieudonné, Boutet de Monvel, and Grisvard. He graduated from Nice in 1972, and obtained his PhD in 1980 from the University of Bordeaux (France), with a thesis entitled Contributions à l'étude des comportements des solutions d'équations différentielles à retard par des méthodes de monotonie et bifurcation.

He joined the ‘Université de Pau et des pays de l'Adour’ (France) in 1973, and became a full professor there in 1988. He taught mainly differential calculus, ordinary and partial differential equations as well as dynamical systems. From 1999 he was First Class Research Director in the IRD (‘Institut pour la recherche et le développement’), Paris-Bondy (France).

He held a position of Visiting Professor at the Memphis State University (Memphis, Tennessee, USA), Brigham Young University (Provo, Utah, USA) and Rice University (Houston, Texas, USA), and was tenure-tracked at the University of Mississippi (Oxford, Mississippi, USA). He also visited many universities throughout the world for various lengths of time, for collaborative work and for teaching.

Ovide was a tireless propagator of the field of biomathematics, making great effort to put students in contact with experts. His scientific reputation enabled him to bring almost anyone to a Conference or Summer School that he was organizing. During the last 10 years he led the organization of more than 20 Conferences and Summer Schools. Along with Profs. D. Axelrod and M. Kimmel, he was the instigator of the series of International Conferences on Mathematical Population Dynamics. He participated as plenary speaker, invited speaker, member of the scientific committee, member of the organizing committee and organizer of special sessions in many conferences, seminars and workshops. Between 1991 and 1996 alone, he took part in more than 40.

Not only this, but he was also responsible for connecting many people around the world who otherwise would never have met and worked together. I would like to take this occasion to thank Ovide on behalf of myself and many others for having set us on the road to our collaborations and friendships.

He was a reviewer for many leading mathematical and mathematical biology journals. He also acted as a reviewer for various mathematical indexes, for the NIH and other national scientific organizations. His involvement in the review process often led him to contact the authors directly with suggestions, most of the times refusing any acknowledgement of his contribution.

One of Ovide's characteristics was his generosity in employing his time for the benefit of his collaborators and students. He put in a lot of effort preparing and developing research projects that brought grants and funding for students to travel and stay in research centres. During the last 10 years, he obtained sponsorship and financing for research projects from international public institutions such as CNRS–CNR (France–Morocco), PICASSO (Spain–France), POLONIUM (Poland–France), IFREMER (France), MedCampus (EU), DGXIV (EU).

But one of Ovide's foremost qualities was his involvement with students. Over the last 20 years he was able to direct more than 60 theses (PhD, ‘thèses d’État', ‘thèses de 3^e cycle’), dedicating a great amount of his time to his students, almost to the level of guru for their future development. Many of his students originating from Morocco, Algeria, and other countries in the region, he played a key role in the development of Biomathematics in North Africa. Many of those he trained are now professors, who continued their collaboration with their former teacher, now late friend.

His privileged collaboration with Morocco has produced, among many others activities, the series of international conferences Marrakesh International Conference on Differential Equations, Summer Schools on delay differential equations and his naming as Scientific Coordinator of Centre International sur les Systèmes Dynamiques of Marrakesh.

This enormous ability for organizing and encouraging students was backed by his great scientific capacity, imagination and deep knowledge of mathematics that became known through a long list of publications, over 150, in prestigious scientific journals, inter alia SIAM Review, Nonlinear Analysis T.M.A., J. Diff. Equat., J. Math. Biol., J. Theor. Biol., J. Math. Anal. Appl., Math. Biosci.

His research developed along two different and complementary lines: works with mathematical aim and modelling in population dynamics. The principal theme of his line of thought was going from model to method: after the construction of a mathematical model for the representation of a particular natural process (cell proliferation, larvae stage of fish, etc.) the necessity arises to develop and update new mathematical tools for its theoretical analysis.

His results in the field of delay differential equations stand out: oscillations, functional differential equations in infinite dimensional spaces, state-dependent delay differential equations. His interest in population dynamics developed fundamentally in two large areas: cell proliferation models and fisheries. Some of the problems dealt with from a mathematical point of view involved obtaining asymptotic properties of the solutions, in the framework of semigroup theory of positive operators as well as the application of aggregation of variables methods to models formulated with two time scales.

But not even the brilliance of his professional life can be compared with his human quality. Ovide was much more than a great scientist: he was very much a family man, extremely generous, always ready to lend a helping hand, a great conversationalist, and overall, a tolerant man: strongly seeking and supporting the goodness within each person.

Personally I would like to underline his infinite patience and affability for me at all times, his understanding. On top of all this stands the enormous help he offered me: he was the maestro I turned to, always honorable in our work and never judging me. I owe him my introduction into the field of Biomathematics, as well as allowing me to connect with others in this field. He was my best colleague and influence.

Ovide has left a significant imprint on our lives. The memory of those shared happy moments will stay forever in our hearts.

Ovide is survived by his wife Elizabeth, three sons Julien, Émilien and Lucien, one daughter Lisa and one grandson Samuel.

Rest in peace.

¹ A comprehensive list of Ovide Arino's works is given in the ‘References’ section [1–146].

Bibliographie

[1] C. Delode; O. Arino; J.-P. Penot Champs mesurables d'espaces polonais, C. R. Acad. Sci. Paris, Ser. A–B, Volume 281 (1975) no. 15, p. A617-A620

[2] C. Delode; O. Arino; J.-P. Penot Champs mesurables et multisections, Ann. Inst. H.-Poincaré, Sect. B (N.S.), Volume 12 (1976) no. 1, pp. 11-42

[3] O. Arino; C. Delode; J. Genet Mesure et Intégration. Exercices et problèmes avec solutions, maîtrises de mathématiques, Vuibert, 1976

[4] O. Arino; P. Séguier Solutions périodiques d'équations différentielles à argument retardé. Oscillations autour d'un point stationnaire, conditions suffisantes de non-existence, C. R. Acad. Sci. Paris, Ser. A–B, Volume 284 (1977) no. 3, p. A145-A147

[5] O. Arino; P. Séguier Solutions oscillantes d'équations différentielles autonomes à retard, C. R. Acad. Sci. Paris, Ser. A–B, Volume 287 (1978) no. 8, p. A611-A613

[6] O. Arino; S. Gautier Stabilité d'un ensemble fermé pour une équation différentielle à argument retardé, C. R. Acad. Sci. Paris, Ser. A–B, Volume 287 (1978) no. 16, p. A1101-A1104

[7] O. Arino; P. Séguier Existence of oscillating solutions for certain differential equations with delay, Functional Differential Equations and Approximation of Fixed Points, Proc. Summer School and Conf. Univ. Bonn, Bonn 1978, Springer, 1979, pp. 46-64

[8] O. Arino; P. Séguier Comportement des solutions de $x (t) + f (t, x (t)) = f (t - 1, x (t - 1))$ , C. R. Acad. Sci. Paris, Ser. A–B, Volume 288 (1979) no. 20, p. A937-A939

[9] O. Arino; P. Séguier Quelques résultats de comportement des solutions d'une classe d'équations différentielles à argument retardé, Functional Differential Systems and Related Topics, Proc. First Int. Conf. Blazejewko, 1979, Higher College Engrg., Zielona Gora, 1980, pp. 34-48

[10] O. Arino; K. Khouk Comportement des solutions d'équations différentielles à retard dans un espace ordonné, C. R. Acad. Sci. Paris, Ser. A–B, Volume 290 (1980) no. 21, p. A1009-A1011

[11] O. Arino The behaviour at the infinity of the solutions of some linear equations with delay is characterized by special solutions of the adjoint equation, Functional-Differential Systems and Related Topics, Proc. First Int. Conf. Blazejewko, 1979, Higher College Engrg., Zielona Gora, 1980, pp. 28-33

[12] O. Arino; I. Gyori Intégration asymptotique des systèmes différentiels fonctionnels asymptotiquement autonomes, C. R. Acad. Sci. Paris, Ser. I, Volume 295 (1982) no. 2, pp. 87-89

[13] M. Kimmel; O. Arino Complex proliferative systems. Formal description and qualitative analysis, Syst. Sci., Volume 9 (1983) no. 1–2, pp. 135-161

[14] O. Arino; P. Séguier About the behaviour at infinity of solutions of $x (t) = f (t - 1, x (t - 1)) - f (t, x (t))$ , J. Math. Anal. Appl., Volume 96 (1983) no. 2, pp. 420-436

[15] E. Ait-Dads; O. Arino Asymptotic almost periodicity of the solutions of some retarded differential equations, Functional-Differential Systems and Related Topics, III (Blazejewko), Higher College Engrg., Zielona Gora, 1983, pp. 45-55

[16] O. Arino; P. Séguier Some results on the solution's behaviour at the infinity, Ninth Int. Conf. on Nonlinear Oscillations, Kiev, 1981, vol. 2, Naukova Dumka, 466, Kiev, 1984, pp. 29-31

[17] O. Arino; F. Hanebaly Remarque sur le théorème de Mawhin–Willem, Ninth Int. Conf. on Nonlinear Oscillations, Kiev, 1981, vol. 2, Naukova Dumka, 466, 1984, pp. 26-29

[18] O. Arino; I. Gyori; A. Jawhari Oscillation criteria in delay equations, J. Diff. Equat., Volume 53 (1984) no. 1, pp. 115-123

[19] O. Arino; S. Gautier; J.-P. Penot A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkcial. Ekvac., Volume 27 (1984) no. 3, pp. 273-279

[20] O. Arino; M. Kimmel Asymptotic analysis of a functional-integral equation related to cell population kinetics, Trends in the Theory and Practice of Nonlinear Analysis, Arlington, Texas, 1984, North-Holland, Amsterdam, 1985, pp. 27-32

[21] O. Arino; T.A. Burton; J.R. Haddock Periodic solutions to functional-differential equations, Proc. R. Soc. Edinb. Sect. A, Volume 101 (1985) no. 3–4, pp. 253-271

[22] O. Arino; T.A. Burton; J.R. Haddock Attractivité de la solution périodique d'une classe d'équations non linéaires du type Volterra, C. R. Acad. Sci. Paris, Ser. I, Volume 300 (1985) no. 15, pp. 517-520

[23] O. Arino; M. Kimmel Stability analysis of models of cell production systems, Math. Model., Volume 7 (1986) no. 9–12, pp. 1269-1300

[24] O. Arino Estimates for periodic solutions of differential equations, Appl. Anal., Volume 21 (1986) no. 4, pp. 307-337

[25] O. Arino; G. Ladas; Y.G. Sficas On oscillations of some retarded differential equations, SIAM J. Math. Anal., Volume 18 (1987) no. 1, pp. 64-73

[26] O. Arino; M. Kimmel Asymptotic analysis of a cell cycle model based on unequal division, SIAM J. Appl. Math., Volume 47 (1987) no. 1, pp. 128-145

[27] O. Arino; E. Haourigui On the asymptotic behaviour of solutions of some delay differential systems which have a first integral, J. Math. Anal. Appl., Volume 122 (1987) no. 1, pp. 36-46

[28] O. Arino; I. Gyori Stability results based on Gronwall type inequalities for some functional-differential systems, Differential Equations: Qualitative Theory, Szeged, 1984, vols. I & II, North-Holland, Amsterdam, 1987, pp. 37-59

[29] M. Kimmel; O. Arino On active linear compartments, in: Mathematical modelling in science and technology, St. Louis, MO, 1987, Math. Comput. Model., Volume 11 (1988), pp. 1189-1194

[30] A. Guessab; G.V. Milovanovic; O. Arino Extremal problems for nonnegative polynomials in $L^{r}$ norm with generalized Laguerre weight, Facta Univ. Ser. Math. Inform., Volume 3 (1988), pp. 1-8

[31] A. Ben M'Barek; O. Arino An integrability criterion for nonforced, nonlinear differential equations, Radiat. Mater., Volume 4 (1988) no. 2, pp. 261-268

[32] O. Arino; E. Hanebaly Solutions presque périodiques de: $(d x / d t) + x a x = h (t)$ $(α ⩾ 0)$ sur les espaces Banach, C. R. Acad. Sci. Paris, Ser. I, Volume 306 (1988) no. 16, pp. 707-710

[33] O. Arino; F. Bourad; N. Hassani Un résultat sur le comportement asymptotique des solutions de systèmes dynamiques monotones, C. R. Acad. Sci. Paris, Ser. I, Volume 307 (1988) no. 7, pp. 311-315

[34] O. Arino, R. Benkhalti, Periodic solutions for $x (t) = λ f (x (t), x (t - 1))$ , Proc. R. Soc. Edinb., Sect. A 109 (3–4) 245–260

[35] O. Arino A note on: ‘On oscillation of solutions of forced functional-differential equations of second order’, Math. Nachr., Volume 122 (1985), pp. 289-300 (MR 88b: 34100] by D.C. Angelova and D.D. Bainov Math. Nachr., 139, 1988, pp. 303-307)

[36] M. Kimmel; O. Arino A system of differential equations modelling the G1 phase of the cell cycle, Comput. Math. Appl., Volume 18 (1989) no. 10–11, pp. 907-917

[37] O. Arino; A. Mortabit A periodicity result for a nonlinear functional integral equation, Proc. Conf. on Optimization and Convex Analysis, Oxford, MS, 1989, Univ. Mississipi, 1989, pp. 1-11

[38] O. Arino; M. Kimmel On some nonlinear effects in a model of population dynamics, Differential equations and applications, vols. I & II, Columbus, OH, 1988, Ohio Univ. Press, Athens, OH, 1989, pp. 20-25

[39] O. Arino; M. Kimmel Asymptotic behaviour of a nonlinear functional-integral equation of cell kinetics with unequal division, J. Math. Biol., Volume 27 (1989) no. 3, pp. 341-354

[40] O. Arino; I. Gyori Necessary and sufficient condition for oscillation of a neutral differential system with several delays, J. Diff. Equat., Volume 81 (1989) no. 1, pp. 98-105

[41] O. Arino; I. Gyori Asymptotic integration of delay differential systems, J. Math. Anal. Appl., Volume 138 (1989) no. 2, pp. 311-327

[42] O. Arino; J.M. Ferreira Total oscillatory behaviour globally in the delays, Port. Math., Volume 46 (1989) no. 1, pp. 71-86

[43] O. Arino; A. Chérif Forced oscillations for Hamiltonian systems, Differential Equations (Xanthi, 1987), 1989, pp. 25-32

[44] O. Arino; A. Chérif An exact formula for the branch of periodic-4-solutions of $x = - λ f (x (t - 1))$ which bifurcates at $λ = π / 2$ , Diff. Integ. Equat., Volume 2 (1989) no. 2, pp. 162-169

[45] E. Ait Dads; O. Arino A nonlinear delay differential equation whose solutions are asymptotically sums of periodic functions, Funkcial. Ekvac., Volume 32 (1989) no. 1, pp. 81-89

[46] O. Arino; M.L. Hbid Periodic solutions for retarded differential systems close to ordinary ones, Nonlinear Anal. T.M.A., Volume 14 (1990) no. 1, pp. 23-34

[47] O. Arino; A. Chérif Un système différentiel ordinaire qui fournit des solutions périodiques d'une équation à retard, C. R. Acad. Sci. Paris, Ser. I, Volume 311 (1990) no. 9, pp. 511-514

[48] O. Arino; F. Bourad On the asymptotic behaviour of the solutions of a class of scalar neutral equations generating a monotone semi-flow, J. Diff. Equat., Volume 87 (1990) no. 1, pp. 84-95

[49] O. Arino; A. Ben M'Barek Periodic solutions of a system of differential equations of first order with discontinuous coefficients, Facta Univ. Ser. Math. Inf., Volume 5 (1990), pp. 57-66

[50] E. Sánchez; O. Arino; M. Kimmel Noncompact semigroups of operators generated by cell kinetics models, Diff. Integ. Equat., Volume 4 (1991) no. 6, pp. 1233-1249

[51] M. Kimmel; O. Arino Cell cycle kinetics with supramitotic control, two cell types, and unequal division: a model of transformed embryonic cells, Math. Biosci., Volume 105 (1991) no. 1, pp. 47-79

[52] O. Arino; K. Niri Oscillations in vector spaces: a comparison result for monotone delay differential systems, J. Math. Anal. Appl., Volume 160 (1991) no. 1, pp. 267-283

[53] O. Arino; A. Mortabit Slow oscillations in a model of cell population dynamics, Mathematical Population Dynamics, Marcel Dekker, 1991, pp. 13-25

[54] O. Arino; M. Kimmel; M. Zerner Analysis of a cell population model with unequal division and random transition, Mathematical Population Dynamics, Marcel Dekker, 1991, pp. 3-12

[55] O. Arino; M. Kimmel Asymptotic behaviour of nonlinear semigroup describing a model of selective cell growth regulation, J. Math. Biol., Volume 29 (1991) no. 4, pp. 283-314

[56] O. Arino Monotone semi-flows which have a monotone first integral, Lect. Notes Math., Volume 1475 (1991), pp. 64-75

[57] O. Arino; A. Mortabit A periodicity result for a nonlinear functional integral equation, J. Math. Biol., Volume 30 (1992) no. 5, pp. 437-456

[58] O. Arino; A. Chérif On the existence of periodic solutions for a class of nonlinearly forced systems, Funkcial. Ekvac., Volume 35 (1992) no. 3, pp. 485-503

[59] O. Arino; R. Benkhalti Bifurcation properties for a sequence of approximation of delay equations, J. Math. Anal. Appl., Volume 171 (1992) no. 2, pp. 377-388

[60] O. Arino; A. Ben M'Barek Uniqueness of periodic solutions of a second-order ODE implied by jump discontinuities of the coefficients, Recent trends in differential equations, World Sci. Pub., River Edge, NJ, 1992, pp. 31-45

[61] O. Arino Some spectral properties for the asymptotic behaviour of semigroups connected to population dynamics, SIAM Rev., Volume 34 (1992) no. 3, pp. 445-476

[62] A. Bouzinab; O. Arino On the existence and uniqueness for an age-dependent population model with nonlinear growth, Facta Univ. Ser. Math. Inf. (1993) no. 8, pp. 55-68

[63] O. Arino; M. Kimmel Comparison of approaches to modeling of cell population dynamics, SIAM J. Appl. Math., Volume 53 (1993) no. 5, pp. 1480-1504

[64] O. Arino; A. Chérif More on ordinary differential equations which yield periodic solutions of delay differential equations, J. Math. Anal. Appl., Volume 180 (1993) no. 2, pp. 361-385

[65] O. Arino A note on the discrete Lyapunov function for scalar differential delay equations, J. Diff. Equat., Volume 104 (1993) no. 1, pp. 169-181

[66] L. Alaoui; O. Arino Compactness and spectral properties for positive translation semigroups associated to models of population dynamics, Diff. Integr. Equat., Volume 6 (1993) no. 2, pp. 459-480

[67] M. Adimy; O. Arino Bifurcation de Hopf globale pour des équations à retard par des semigroupes intégrés, C. R. Acad. Sci. Paris, Ser. I, Volume 317 (1993) no. 8, pp. 767-772

[68] M. Kimmel; O. Arino Two simple models of almost the same population with very different dynamics, Math. Biosci., Volume 122 (1994) no. 2, pp. 183-200

[69] O. Arino; M. Kimmel A nondifferentiable semigroup generated by a model of cell population dynamics, Appl. Math. Comput. Sci., Volume 4 (1994) no. 2, pp. 211-221

[70] O. Arino; M.L. Hbid Poincaré procedure for an ordinary differential system perturbed by a functional term, Diff. Equat. Dyn. Syst., Volume 2 (1994) no. 2, pp. 113-120

[71] O. Arino; M.A. El Attar A proof of characterization of oscillation for higher-order neutral differential equations of mixed type by the Laplace transform, Proc. R. Soc. Edinb., Sect. A, Volume 124 (1994) no. 5, pp. 909-916

[72] A. Boussoir; O. Arino; S. Gautier The necessary and sufficient conditions for the integral of a multivalued map to be a polygon, Appl. Math. Comput. Sci., Volume 5 (1995) no. 4, pp. 657-669

[73] T. Benouaz; O. Arino Determination of the stability of a nonlinear ordinary differential equation by least square approximation. Computational procedure, Appl. Math. Comput. Sci., Volume 5 (1995) no. 1, pp. 33-48

[74] O. Arino; E. Sánchez Linear theory of abstract functional-differential equations of retarded type, J. Math. Anal. Appl., Volume 191 (1995) no. 3, pp. 547-571

[75] O. Arino; M.L. Hbid Sur l'unicité des solutions périodiques du système différential à retard $d x / d t = f (x (t - r)), x \in R$ , Facta Univ. Ser. Math. Inf., Volume 10 (1995), pp. 71-79

[76] O. Arino; M.A. El Attar Necessary and sufficient condition for the oscillation of higher-order neutral differential system with several delays, Facta Univ. Ser. Math. Inf., Volume 10 (1995), pp. 81-86

[77] M. Kimmel; O. Arino; D.E. Axelrod Backward/forward duality of branching processes and cell population dynamics, Differential equations and applications to biology and to industry, Claremont, CA, 1994, World Sci. Pub., River Edge, NJ, 1996, pp. 233-240

[78] T. Benouaz; O. Arino Least-square approximation of a nonlinear ordinary differential equation, Comput. Math. Appl., Volume 31 (1996) no. 8, pp. 69-84

[79] O. Arino; E. Sánchez A variation of constants formula for an abstract functional-differential equation of retarded type, Diff. Integr. Equat., Volume 9 (1996) no. 6, pp. 1305-1320

[80] O. Arino; K. Niri Subdominant behaviour in positive semigroups: the case of a class of delay differential equations, Diff. Equat. Dyn. Syst., Volume 4 (1996) no. 1, pp. 99-111

[81] O. Arino; K. Khouk The delay effects on the behaviour of solutions of reaction diffusion equations with delay, Appl. Anal., Volume 61 (1996) no. 3–4, pp. 195-208

[82] O. Arino; M.L. Hbid Existence of periodic solutions for a delay differential equation via the Poincaré procedure, Diff. Equat. Dyn. Syst., Volume 4 (1996) no. 2, pp. 125-148

[83] O. Arino; I. Gyori; M. Pituk Asymptotically diagonal delay differential systems, J. Math. Anal. Appl., Volume 204 (1996) no. 3, pp. 701-728

[84] O. Arino; M. Bahaj Periodic and almost periodic solutions of differential equations in Banach spaces, Nonlinear Anal. T.M.A., Volume 26 (1996) no. 2, pp. 335-341

[85] E. Ait Dads; K. Ezzinbi; O. Arino Positive almost periodic solutions for some nonlinear delay integral equation, Nonlinear Stud., Volume 3 (1996) no. 1, pp. 85-101

[86] E. Ait Dads; K. Ezzinbi; O. Arino Existence of periodic solution for some neutral nonlinear integral equation with delay time dependent, Facta Univ. Ser. Math. Inform., Volume 11 (1996), pp. 79-92

[87] E. Ait Dads; O. Arino Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations, Nonlinear Anal. T.M.A., Volume 27 (1996) no. 4, pp. 369-386

[88] K. Pakdaman; C.P. Malta; C. Grotta-Ragazzo; O. Arino; J.-F. Vibert Transient oscillations in continuous time excitatory ring neural networks with delay, Phys. Rev. E(3), Volume 55 (1997) no. 3, B, pp. 3234-3248

[89] O. Arino; E. Sánchez; G.F. Webb Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence, J. Math. Anal. Appl., Volume 215 (1997) no. 2, pp. 499-513

[90] O. Arino; E. Sánchez; G.F. Webb Polynomial growth dynamics of telomere loss in a heterogeneous cell population, Dynam. Contin. Discrete Impuls. Syst., Volume 3 (1997) no. 3, pp. 263-282

[91] O. Arino; E. Sánchez A survey of cell population dynamics, J. Theor. Med., Volume 1 (1997) no. 1, pp. 35-51

[92] O. Arino; R. Benkhalti; K. Ezzinbi Existence results for initial value problems for neutral functional-differential equations, J. Diff. Equat., Volume 138 (1997) no. 1, pp. 188-193

[93] Advances in mathematical population dynamics: molecules, cells and man, Papers from the International Conference on Mathematical Population Dynamics held at Rice Univ. Houston, TX (O. Arino; D. Axelrod; M. Kimmel, eds.), World Scientific Pub. Co. Inc., River Edge, NJ, May 23–27, 1997

[94] E. Ait Dads; K. Ezzinbi; O. Arino Pseudo almost periodic solutions for some differential equations in a Banach space, Nonlinear Anal. T.M.A., Volume 28 (1997) no. 7, pp. 1141-1155

[95] M. Ait Babram; M.L. Hbid; O. Arino Approximation scheme of a center manifold for functional-differential equations, J. Math. Anal. Appl., Volume 213 (1997) no. 2, pp. 554-572

[96] N. Yousfi; O. Arino Invariant cone of slowly ocillating solution in two delays differential equations, Acta Math. Univ. Comenian (N.S.), Volume 67 (1998) no. 2, pp. 335-342

[97] T. Benouaz; O. Arino Optimal approximation of the initial value problem, Comput. Math. Appl., Volume 36 (1998) no. 1, pp. 21-32

[98] O. Arino; W.V. Smith Migration in age structured population dynamics, Math. Models Methods Appl. Sci., Volume 8 (1998) no. 5, pp. 905-925

[99] O. Arino; E. Sánchez; R. Bravo de la Parra A model of an age-structured population in a multipatch environment, Math. Comput. Model., Volume 27 (1998) no. 4, pp. 137-150

[100] O. Arino; E. Sánchez An integral equation of cell population dynamics formulated as an abstract delay equation. Some consequences, Math. Models Methods Appl. Sci., Volume 8 (1998) no. 4, pp. 713-735

[101] O. Arino; M. Pituk Asymptotic constancy for neutral functional-differential equations, Diff. Equat. Dyn. Syst., Volume 6 (1998) no. 3, pp. 261-273

[102] O. Arino; V.R. Nosov On stability of a class of neutral type functional-differential equations, Math. Comput. Simul., Volume 45 (1998) no. 3–4, pp. 299-307

[103] O. Arino; M.L. Hbid; R. Bravo de la Parra A mathematical model of growth of population of fish in the larval stage: density-dependent effects, Math. Biosci., Volume 150 (1998) no. 1, pp. 1-20

[104] O. Arino; K.P. Hadeler; M.L. Hbid Existence of periodic solutions for delay differential equations with state-dependent delay, J. Diff. Equat., Volume 144 (1998) no. 2, pp. 263-301

[105] E. Ait Dads; K. Ezzinbi; O. Arino Periodic and almost periodic results for some differential equations in Banach spaces, Nonlinear Anal., Volume 31 (1998) no. 1–2, pp. 163-170

[106] N. Yousfi; O. Arino Slowly oscillating solutions of differential equations with delays, Northeast Math. J., Volume 15 (1999) no. 2, pp. 217-222

[107] C. Jost; O. Arino; R. Arditi About deterministic extinction in ratio-dependent predator-prey models, Bull. Math. Biol., Volume 61 (1999) no. 1, pp. 19-32

[108] A. De Gaetano; O. Arino Probabilistic determination of stability for a delay-differential model of the glucose-insulin dynamical system, J. Biol. Syst., Volume 7 (1999) no. 2, pp. 131-144

[109] J. Chattopadhyay; O. Arino A predator–prey model with disease in prey, Nonlinear Anal., Volume 36 (1999), pp. 747-766

[110] R. Bravo de la Parra; E. Sánchez; O. Arino; P. Auger A discrete model with density dependent fast migration, Math. Biosci., Volume 157 (1999) no. 1–2, pp. 91-109

[111] O. Arino; W.V. Smith A nonlinear model for migrating species, J. Math. Anal. Appl., Volume 229 (1999) no. 1, pp. 61-87

[112] O. Arino; O. Sidki An abstract neutral functional-differential equation arising from a cell population model, J. Math. Anal. Appl., Volume 235 (1999) no. 2, pp. 435-453

[113] O. Arino; E. Sánchez; R. Bravo de la Parra; P. Auger A singular perturbation in an age-structured population model, SIAM J. Appl. Math., Volume 60 (1999) no. 2, pp. 408-436

[114] O. Arino; M. Pituk Convergence in asymptotically autonomous functional-differential equations, J. Math. Anal. Appl., Volume 237 (1999) no. 1, pp. 376-392

[115] O. Arino; I. Gyor Qualitative properties of the solutions of delay differential equations with impulses. I. Stability, Diff. Equat. Dyn. Syst., Volume 7 (1999) no. 1, pp. 21-37

[116] O. Arino; I. Gyori Qualitative properties of the solutions of a delay differential equation with impulses. II. Oscillations, Diff. Equat. Dyn. Syst., Volume 7 (1999) no. 2, pp. 161-179

[117] O. Arino; A. Berboucha Estimations sur des solutions globales d'équations différentielles ordinaires, Ann. Math. Univ. Sidi Bel Abbès, Volume 6 (1999), pp. 159-170

[118] P. Magal; O. Arino Existence of periodic solutions for a state dependent delay differential equation, J. Diff. Equat., Volume 165 (2000) no. 1, pp. 61-95

[119] A. Lakmeche; O. Arino Bifurcation of non-trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dyn. Contin. Discrete Impuls. Syst., Volume 7 (2000) no. 2, pp. 265-287

[120] M. Khaladi; O. Arino Estimation of the rate of convergence of semigroups to an asynchronous equilibrium, Semigroup Forum, Volume 61 (2000) no. 2, pp. 209-223

[121] A. De Gaetano; O. Arino Mathematical modelling of the intravenous glucose tolerance test, J. Math. Biol., Volume 40 (2000) no. 2, pp. 136-168

[122] R. Bravo de la Parra; O. Arino; E. Sánchez; P. Auger A model for an age-structured population with two time scales, Proc. Conf. on Dynamical Systems in Biology and Medicine (Veszprem, 1997), vol. 31, 2000, pp. 17-26

[123] O. Arino; J.A. Montero-Sánchez Optimal control of a non-linear elliptic population system, Proc. Edinb. Math. Soc. (2), Volume 43 (2000) no. 2, pp. 225-241

[124] O. Arino; K. Boushaba; A. Boussouar A mathematical model of the dynamics of the phytoplankton–nutrient system, Nonlinear Anal. Real World Appl., Volume 1 (2000) no. 1, pp. 69-87

[125] E. Ait Dads; K. Ezzinbi; O. Arino Periodic and almost periodic solutions for some delay integral equations in a Hilbert space, Diff. Equat. Dyn. Syst., Volume 8 (2000) no. 3–4, pp. 193-212

[126] O. Sidki; O. Arino On semigroups of nonlinear operators and the solution of the functional differential equations, Dyn. Contin. Discrete Impuls. Syst., Ser. A Math. Anal., Volume 8 (2001) no. 2, pp. 249-259

[127] Ramzi; O. Arino; C. Koutsikopoulos; A. Boussouar; P. Lazure Modelling and numerical simulations of larval migration of the sole (Solea solea (L.)) of the Bay of Biscay. Part 2: Numerical simulations, Oceanol. Acta, Volume 24 (2001) no. 2, pp. 113-124

[128] Ramzi; O. Arino; C. Koutsikopoulos; A. Boussouar; P. Lazure Modelling and numerical simulations of larval migration of the sole (Solea solea (L.)) of the Bay of Biscay. Part 1: Modelling, Oceanol. Acta, Volume 24 (2001) no. 2, pp. 101-112

[129] O. Pardo; O. Arino Weight-controlled recruitment of the anchovy in the late larval stage, Nat. Resour. Model., Volume 14 (2001) no. 2, pp. 257-286

[130] A. Lakmeche; O. Arino Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors, Nonlinear Anal. Real World Appl., Volume 2 (2001) no. 4, pp. 455-465

[131] T. Krisztin; O. Arino The two-dimensional attractor of a differential equation with state-dependent delay, J. Dyn. Diff. Equat., Volume 13 (2001) no. 3, pp. 453-522

[132] M. El Massoud; O. Arino The ideal thermocline equations, Actes des VIes Journées Zaragoza–Pau de mathématiques appliquées et de statistiques, Jaca, 1999, Publ. Univ. Pau, 2001, pp. 193-199

[133] A. Boussouar; S. Le Bihan; O. Arino; P. Prouzet Mathematical model and numerical simulations of the migration and growth of Biscay Bay anchovy early larval stages, Oceanol. Acta, Volume 24 (2001) no. 5, pp. 489-504

[134] Bobrowski; M. Kimmel; O. Arino; R. Chakraborty A semigroup representation and asymptotic behavior of certain statistics of the Fisher-Wright-Moran coalescent, Stochastic processes: theory and methods, North-Holland, 2001, pp. 215-247

[135] O. Arino; E. Sánchez; A. Fathallah State-dependent delay differential equations in population dynamics: modeling and analysis, Topics in functional differential and difference equations (Lisbon, 1999), Am. Math. Soc., 2001, pp. 19-36

[136] O. Arino; M. Pituk More on linear differential systems with small delays, J. Diff. Equat., Volume 170 (2001) no. 2, pp. 381-407

[137] M. Ait Babram; O. Arino; M.L. Hbid Computational scheme of a center manifold for neutral functional differential equations, J. Math. Anal. Appl., Volume 258 (2001) no. 2, pp. 396-414

[138] M. Louihi; M.L. Hbid; O. Arino Semigroup properties and the Crandall–Liggett approximation for a class of differential equations with state-dependent delays, J. Diff. Equat., Volume 181 (2002) no. 1, pp. 1-30

[139] A. El Abdallaoui; J. Chattopadhyay; O. Arino Comparisons, by models, of some basic mechanisms acting on the dynamics of the zooplankton-toxic phytoplankton system, Math. Models Methods Appl. Sci., Volume 12 (2002) no. 10, pp. 1421-1451

[140] K. Boushaba; O. Arino; A. Boussouar A mathematical model for phytoplankton, Math. Models Methods Appl. Sci., Volume 12 (2002) no. 6, pp. 871-901

[141] S. Portet; O. Arino; J. Vassy; D. Schoevaert Organization of the cytokeratin network in an epithelial cell, J. Theor. Biol., Volume 223 (2003), pp. 313-333

[142] R. Ouifki; M.L. Hbid; O. Arino Attractiveness and Hopf bifurcation for retarded differential equations, Commun. Pure Appl. Anal., Volume 2 (2003) no. 2, pp. 147-158

[143] M. Bachar; O. Arino Integrated semigroup and linear ordinary differential equation with impulses, Fields Inst. Commun., Am. Math. Soc., Volume 36 (2003), pp. 17-31

[144] M. Adioui; J.-P. Treuil; O. Arino Alignment in a fish school: a mixed Lagrangian–Eulerian approach, Ecol. Model., Volume 167 (2003), pp. 19-32

[145] M. Adioui; O. Arino; W.V. Smith; J.-P. Treuil A mathematical analysis of a fish school model, J. Diff. Equat., Volume 188 (2003) no. 2, pp. 406-446

[146] A. Mukhopadhyay; A. De Gaetano; O. Arino Modeling the intra-venous glucose tolerance test: a global study for a single-distributed-delay model, Discrete Contin. Dyn. Syst., Ser. B, Volume 4 (2004) no. 2, pp. 407-417

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