Perturbation par dualité, interprétation par la théorie des semi-groupes intégrés, application à l'étude du problème de bifurcation de Hopf dans le cadre des équations à retard, Thèse de doctorat à Pau, 1991. ,
A singular transport model describing cellular division, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.12 ,
DOI : 10.1016/S0764-4442(01)01929-2
Résultats de stabilité pour une équation semi-linéaire de transport singulière décrivant une division cellulaire, 2001. ,
modèle de transport singulier décrivant une division cellulaire avec une phase de polifération croissante par rapport à la maturité, 2001. ,
The abstract Cauchy problem, special semigroups and perturbation, 1184. ,
Asymptotic Analysis of a Cell Cycle Model Based on Unequal Division, SIAM Journal on Applied Mathematics, vol.47, issue.1, pp.128-145, 1987. ,
DOI : 10.1137/0147008
Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division, Journal of Mathematical Biology, vol.85, issue.3, pp.341-354, 1989. ,
DOI : 10.1007/BF00275817
Asymptotic behavior of nonlinear semigroup describing a model of selective cell growth regulation, Journal of Mathematical Biology, vol.85, issue.4, pp.289-314, 1991. ,
DOI : 10.1007/BF00167154
Comparison of Approaches to Modeling of Cell Population Dynamics, SIAM Journal on Applied Mathematics, vol.53, issue.5, pp.1480-1504, 1993. ,
DOI : 10.1137/0153069
Necessary and su¢cient conditions for asynchronous exponential growth in age structured cell populations with quiescence, J. Math ,
A singular perturbation in an age-structured population model, SIAM J. Appl. Math, vol.60, issue.2, pp.408-436, 1999. ,
Structured Cell population dynamics, lecture for the European School on Mathematics and cell physiology and proliferation, 1999. ,
On Devaney's Definition of Chaos, The American Mathematical Monthly, vol.99, issue.4, pp.332-339, 1992. ,
DOI : 10.2307/2324899
Introduction to Operator Theory and Invariant Subspaces, 1988. ,
Stability analysis of an age-structured model with a state dependent delay, Can. Applied Math. Quart, vol.6, issue.4, 1997. ,
Age-structured and two-delay models for erythropoiesis, Mathematical Biosciences, vol.128, issue.1-2, pp.317-346, 1995. ,
DOI : 10.1016/0025-5564(94)00078-E
Cell Growth and Division, Biophysical Journal, vol.8, issue.4, pp.431-444, 1968. ,
DOI : 10.1016/S0006-3495(68)86498-7
Cell growth and division. I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures ,
The Asymptotic Behavior of a Transport Equation in Cell Population Dynamics with a Null Maturation Velocity, Journal of Mathematical Analysis and Applications, vol.243, issue.1, pp.47-63, 2000. ,
DOI : 10.1006/jmaa.1999.6650
-PHASE IN THE CELL CYCLE, Cell Proliferation, vol.8, issue.4, pp.321-334, 1970. ,
DOI : 10.1016/0014-4827(59)90063-1
URL : https://hal.archives-ouvertes.fr/hal-01057010
Asymptotic Behavior of an Age-Structured Population Model and Optimal Maturation Age, Journal of Mathematical Analysis and Applications, vol.233, issue.2, pp.808-826, 1999. ,
DOI : 10.1006/jmaa.1999.6350
The theory of ?uctuations in brightness of the Milky- Way, Astrophys. J, vol.125, pp.94-123, 1997. ,
Delay di¤erential equations, cours à Pomona College ,
Dependence on initial conditions in nonlocal PDE's and hereditary dynamical systems, Proc. Inter. Conf. Nonlin. Anal, pp.3125-3136, 1996. ,
DOI : 10.1515/9783110883237.3125
Propagating fronts, chaos and multistability in a cell replication model, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.6, issue.3, pp.477-492, 1996. ,
DOI : 10.1063/1.166195
Lecture notes in Biomathematics, pp.90-96, 1982. ,
On the stability of the cell size distribution, Journal Of Mathematical Biology, vol.5, issue.2, pp.227-248, 1984. ,
DOI : 10.1007/BF00277748
Growth, fission and the stable size distribution, Growth, ?ssion and the stable size distribution, pp.135-148, 1983. ,
DOI : 10.1007/BF00280662
A singular transport equation modelling a proliferating maturity structured cell population, Can. Appl. Math. Quart, vol.4, pp.65-95, 1996. ,
A singular transport equation with delays, Proc. Second International Conference on Di¤erential Equations in Marrakesh, 1996. ,
Hypercyclicity of solutions of a transport equation with delays, Nonlinear Analysis: Theory, Methods & Applications, vol.29, issue.12, pp.1343-1351, 1997. ,
DOI : 10.1016/S0362-546X(96)00192-7
An age and maturity structured model of cell population dynamics, Mathematical Models in Medical and Health Science, pp.99-116, 1998. ,
A Nonlinear Age and Maturity Structured Model of Population Dynamics, Journal of Mathematical Analysis and Applications, vol.242, issue.1, pp.93-104, 2000. ,
DOI : 10.1006/jmaa.1999.6656
A Nonlinear Age and Maturity Structured Model of Population Dynamics, Journal of Mathematical Analysis and Applications, vol.242, issue.2, pp.255-270, 2000. ,
DOI : 10.1006/jmaa.1999.6657
A maturity structured model of a population of proliferating and quiescent cells ,
ON THE RESTING PERIODS IN THE CELL LIFE CYCLE, Cell Proliferation, vol.17, issue.1, pp.75-93, 1969. ,
DOI : 10.1016/0012-1606(67)90004-8
One parameter semigroups for linear evolution equations, Graduate texts in mathematics, 1999. ,
L'application de la transformée de Laplace aux équations di¤érentielles à retard en dimension ?nie et in?nie (analyse mathématique, Thèse Univ. de Pau et des Pays de l, 1999. ,
Limit theorems for Markov processes, Transactions of the American Mathematical Society, vol.121, issue.1, pp.200-209 ,
DOI : 10.1090/S0002-9947-1966-0185642-8
The Ergodic theory of Markov Processes, 1969. ,
Statistics and dynamics of procaryotic cell populations, Mathematical Biosciences, vol.1, issue.3, pp.327-374, 1967. ,
DOI : 10.1016/0025-5564(67)90008-9
Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière, Mathématiques et Applications, vol.22, 1995. ,
Operators with dense, invariant, cyclic vector manifolds, Journal of Functional Analysis, vol.98, issue.2, pp.229-269, 1991. ,
DOI : 10.1016/0022-1236(91)90078-J
An age-dependent population dynamical model with a small parameter, Mathematical and Computer Modelling, vol.31, issue.4-5, pp.63-72, 2000. ,
DOI : 10.1016/S0895-7177(00)00022-4
GROWTH OF CELL POPULATIONS VIA ONE-PARAMETER SEMIGROUPS OF POSITIVE OPERATORS, Mathematics Applied to Science, pp.79-104, 1988. ,
DOI : 10.1016/B978-0-12-289510-4.50012-4
Nonlinear age-dependent population dynamics, Archive for Rational Mechanics and Analysis, pp.281-300, 1974. ,
Nonlinear age-dependent population dynamics in continuously propagated bacterial cultures, Mathematical Biosciences, vol.62, issue.1, pp.45-74, 1982. ,
DOI : 10.1016/0025-5564(82)90062-1
An abstract delay-di¤erential equation modelling size dependent cell growth and division SIAM, J. Math. Anal, vol.18, pp.74-88, 1987. ,
Age-size structure in populations with quiescence, Mathematical Biosciences, vol.86, issue.1, pp.67-95, 1987. ,
DOI : 10.1016/0025-5564(87)90064-2
Quiescence as an explanation of gompertzian tumor growth, Growh Development and Aging, vol.53, pp.25-33, 1989. ,
A nonlinear structured population model of tumor growth with quiescence, Journal of Mathematical Biology, vol.18, issue.6, pp.671-694, 1990. ,
DOI : 10.1007/BF00160231
Quiescence in structured population dynamics, Lecture Notes in Pure and Applied Mathematics, vol.131, pp.45-62, 1991. ,
Asynchronous exponential growth of semigroups of nonlinear operators, Journal of Mathematical Analysis and Applications, vol.167, issue.2, pp.443-467, 1992. ,
DOI : 10.1016/0022-247X(92)90218-3
Theory of functional di¤erential equations, 1977. ,
Steady-State Size Distributions in Probabilistic Models of the Cell Division Cycle, SIAM Journal on Applied Mathematics, vol.45, issue.4, pp.523-540, 1985. ,
DOI : 10.1137/0145031
On the stable size distribution of populations reproducing by ?ssion into two unequal parts, Mathematical Biosciences, vol.72, pp.196-50, 1984. ,
An eigenvalue problem related to cell growth, Journal of Mathematical Analysis and Applications, vol.111, issue.1, pp.253-280, 1985. ,
DOI : 10.1016/0022-247X(85)90215-X
The dynamical behavior of the age-size distribution of a cell population , in The dyamics of physiologically structured populations, Lecture notes in biomathematics, 1986. ,
Structured populations, linear semigroups and positivity, Mathematische Zeitschrift, vol.2, issue.No. 1, pp.599-617, 1986. ,
DOI : 10.1007/BF01162350
Population analysis and models, 1976. ,
Hypercyclic operators and chaos, J. Operator Theory, vol.28, pp.93-103, 1992. ,
Size and maturity structured models of cell population dynamics exhibiting chaotic behavior, thèse, mars, 2000. ,
Synthesis of Desoxyribonucleic Acid in Normal and Irradiated Cells and Its Relation to Chromosome Breakage, International Journal of Radiation Biology and Related Studies in Physics, Chemistry and Medicine, vol.23, issue.1, p.261 ,
DOI : 10.1080/09553008514552501
The cell cycle, 1981. ,
Introduction to the mathematics of population, 1968. ,
Cell cycle kinetics with supramitotic control, two cell types, and unequal division: a model of transformed embryonic cells, Mathematical Biosciences, vol.105, issue.1, pp.47-79, 1991. ,
DOI : 10.1016/0025-5564(91)90048-N
Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis, Journal of Theoretical Biology, vol.110, issue.4, pp.637-664, 1984. ,
DOI : 10.1016/S0022-5193(84)80149-6
Globally asymptotic properties of proliferating cell populations, Journal of Mathematical Biology, vol.70, issue.1, pp.43-62, 1984. ,
DOI : 10.1007/BF00275930
Probabilistic properties of deterministic systems, 1985. ,
DOI : 10.1017/CBO9780511897474
Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, 1994. ,
Stability properties of proliferatively coupled cell replication models, Acta Biotheoretica, vol.53, issue.1, pp.1-14, 1991. ,
DOI : 10.1007/BF00046404
A nonlinear boundary value problem arising in growing cell population, Nonlinear Analysis, pp.843-862, 1999. ,
Uni?ed hypothesis of the origin of aplastic anemia and periodic hematopoiesis, Blood, vol.51, pp.941-956, 1978. ,
Dynamic haematological disorders of stem cell origin, Biophysical and biochemical Information Transfer in recognition, pp.373-409, 1979. ,
Enigmatic hematopoïesis, Biomathematics and cell kinetics, pp.87-103, 1981. ,
Continuous maturation of proliferating erythroid precursors, Cell Proliferation, vol.7, issue.4, pp.381-392, 1982. ,
DOI : 10.1016/0014-4827(79)90526-3
Feedback, delays and the origin of blood cell dynamics, Comm. Theor. Biol, vol.1, pp.299-327, 1990. ,
Global stability in a delayed partial differential equation describing cellular replication, Journal of Mathematical Biology, vol.414, issue.1, pp.89-109, 1994. ,
DOI : 10.1007/BF00160175
A new criterion for the global stability of simultaneous cell replication and maturation processes, Journal of Mathematical Biology, vol.38, issue.3, pp.195-219, 1999. ,
DOI : 10.1007/s002850050146
Hematopoietic model with moving boundary condition and state dependent delay: application in erythropoiesis, J. Theor. Biol, vol.190, pp.135-146, 1998. ,
Asymptotic Behavior in Age-Dependent Population Dynamics with Hereditary Renewal Law, SIAM Journal on Mathematical Analysis, vol.12, issue.6, pp.904-916, 1981. ,
DOI : 10.1137/0512076
The biology of the cell cycle, 1971. ,
The Cell Cycle in the Fission Yeast, Schizosaccharomyces pombe. I. Relationship between Cell Size and Cycle Time, Cell Structure and Function, vol.3, issue.1, pp.39-46, 1978. ,
DOI : 10.1247/csf.3.39
One parameter semigroups of positive operators, Lecture notes in mathematics 1184, 1986. ,
Age Distributions in Dividing Populations, Biophysical Journal, vol.7, issue.1, pp.69-76, 1967. ,
DOI : 10.1016/S0006-3495(67)86575-5
A continuity equation for cell populations, Bull. Math. Biophys, vol.28, pp.545-554, 1966. ,
Mathematics of Microbial Populations, Annual Review of Microbiology, vol.22, issue.1, pp.519-548, 1968. ,
DOI : 10.1146/annurev.mi.22.100168.002511
Semigroups of linear operators and applications to partial di¤erential equations, 1983. ,
Mahematical models for the growth of human populations, 1973. ,
On the spectrum of c 0 ¡ semigroups, Transaction of the A, pp.847-857, 1984. ,
Global stability of cellular populations with unequal division, Canadian Applied Mathematics QuarterlyJournalName, vol.8, issue.2 ,
DOI : 10.1216/camq/1032375042
Bifurcations and traveling waves in a delayed partial differential equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.2, issue.2, pp.231-244, 1992. ,
DOI : 10.1063/1.165909
Multistability and boundary layer development in a transport equation with retarded arguments, Can, Appl. Math. Quart, vol.1, pp.1-21, 1993. ,
Transitions and kinematics of reaction-convection fronts in a cell population model, Physica D: Nonlinear Phenomena, vol.80, issue.1-2, pp.120-139, 1995. ,
DOI : 10.1016/0167-2789(95)90067-5
Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function, Physica D: Nonlinear Phenomena, vol.86, issue.3, pp.373-395, 1995. ,
DOI : 10.1016/0167-2789(95)00114-J
Asynchronous exponential growth in a size structured cell population with quiescent compartment, In population Dynamics: Analysis of heterogeneity, 1995. ,
Quiescence as an explanation for asynchronous exponential growth in a size structured cell population of exponentially growing cells, In Advances Mathematical Population Dynamics, Part I ,
A Maturity-Time Representation for Cell Populations, Biophysical Journal, vol.8, issue.10, pp.1055-1073, 1968. ,
DOI : 10.1016/S0006-3495(68)86539-7
A mathematical model of neutrophil production and control in normal man, Journal of Mathematical Biology, vol.41, issue.3, pp.187-225, 1975. ,
DOI : 10.1111/j.1699-0463.1957.tb01014.x
Analyse réelle et complexe, 1975. ,
Asymptotic behavior of a transport equation, Ann. Pol. Math, vol.57, pp.45-55, 1992. ,
MARKOV SEMIGROUPS AND STABILITY OF THE CELL MATURITY DISTRIBUTION, Journal of Biological Systems, vol.08, issue.01, pp.69-94, 2000. ,
DOI : 10.1142/S0218339000000067
A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer, pp.765-770, 1991. ,
DOI : 10.1090/S0002-9939-1991-1049848-8
Cell cycle progression: computer simulation of uncoupled subcycles of DNA replication and cell growth, Journal of Theoretical Biology, vol.175, issue.2, pp.177-189, 1995. ,
DOI : 10.1006/jtbi.1995.0130
A New Model For Age-Size Structure of a Population, Ecology, vol.48, issue.6, pp.910-918, 1967. ,
DOI : 10.2307/1934533
A Model for Population Reproducing by Fission, Ecology, vol.52, issue.2, pp.330-335, 1971. ,
DOI : 10.2307/1934592
Periodic Solutions of a Nonlinear Age-Dependent Model of Single Species Population Dynamics, SIAM Journal on Mathematical Analysis, vol.11, issue.5, pp.901-910, 1980. ,
DOI : 10.1137/0511080
On the existence of invariant densities for Markov operators, Ann. Polon. Math, vol.48, pp.51-56, 1988. ,
Numerical methods for Volterra functional di¤erential equations, 1969. ,
Markov semigroup generated by Poisson driven di¤erential equations, Bull. Pol. Ac. Math, vol.44, pp.230-252, 1996. ,
Mathematical models for cellular systems: The Von Foerster equation ,
On the average cellular volume in synchronized cell populations, The Bulletin of Mathematical Biophysics, vol.32, issue.4, pp.459-473, 1970. ,
DOI : 10.1007/BF02476765
Sloppy size control of the cell division cycle, Journal of Theoretical Biology, vol.118, issue.4, pp.29-62, 1985. ,
DOI : 10.1016/S0022-5193(86)80162-X
The distributions of cell size and generation time in a model of the cell cycle incorporating size control and random transitions, Journal of Theoretical Biology, vol.113, issue.1, pp.29-62, 1985. ,
DOI : 10.1016/S0022-5193(85)80074-6
Global asymptotic stability of the size distribution in probabilistic models of the cell cycle, Journal of Mathematical Biology, vol.22, issue.1, pp.61-68, 1985. ,
DOI : 10.1007/BF00276546
Cell growth and division: a deterministic/probabilistic model of the cell cycle, Journal of Mathematical Biology, vol.113, issue.2, pp.231-246, 1986. ,
DOI : 10.1007/BF00276959
Asymptotics of new population models with quiescence ,
Sur la théorie mathématique des phénomènes héréditaires, J. Math. Pures Appl, vol.7, pp.249-298, 1928. ,
Théorie mathématique de la lutte pour la vie, 1931. ,
Some remarks on changing populations, The Kinetics of Cellular Proliferation, Grune et Stratton, pp.382-407, 1959. ,
An invariant manifold of slowly oscillating solutions for ² x (t) = ¡¹x (t ) + f (x (t ¡ 1 ), J. Reine Angew. Math, vol.414, pp.67-112, 1991. ,
Autonomous nonlinear functional di¤erential equations and nonlinear semigroups, pp.1-12, 1974. ,
A semigroup proof of the Sharpe-Lotka theorem, Lecture Notes in Mathematics, vol.52, issue.3, pp.254-268, 1983. ,
DOI : 10.1016/0022-247X(75)90067-0
Theory of Nonlinear age-dependent population dynamics, Monographs and Textbooks in Pure and Appl, Math. Series, vol.89, 1985. ,
Random transitions, size control, and inheritance in cell population dynamics, Mathematical Biosciences, vol.85, issue.1, 1987. ,
DOI : 10.1016/0025-5564(87)90100-3
Lectures on chaotic dynamical systems on in?nite dimensional spaces, 1996. ,
Asynchronous Exponential Growth in Transition Probability Models of the Cell Cycle, SIAM Journal on Mathematical Analysis, vol.18, issue.4, pp.897-908, 1987. ,
DOI : 10.1137/0518068
Theory and applications of partial di¤erential equations, Applied Mathematical Sciences, vol.119, 1994. ,