Hopf bifurcation in an Age-Dependent Population Model with delayed Birth Process

This paper is devoted to the study of an age-dependent population system with Riker type birth function. The time lag factor is considered for the birth process. We investigate some dynamical properties of the equation by using C0-semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system.

[1]  Jim M Cushing,et al.  The dynamics of hierarchical age-structured populations , 1994 .

[2]  Fabien Crauste,et al.  Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay , 2010, SIAM J. Appl. Math..

[3]  David M. Auslander,et al.  Dynamics of interacting populations , 1974 .

[4]  Pierre Magal,et al.  Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems , 2008 .

[5]  Sebastian Aniţa,et al.  Analysis and Control of Age-Dependent Population Dynamics , 2010 .

[6]  Weinian Zhang,et al.  An Age-Structured Model for the Transmission Dynamics of Hepatitis B , 2010, SIAM J. Appl. Math..

[7]  J. Farkas,et al.  Asymptotic behavior of size structured populations via juvenile-adult interaction , 2007 .

[8]  R. Nagel The spectrum of unbounded operator matrices with non-diagonal domain , 1990 .

[9]  Junjie Wei,et al.  Periodicity and synchronization in blood-stage malaria infection , 2011, Journal of mathematical biology.

[10]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[11]  Jim M Cushing,et al.  Hierarchical models of intra-specific competition: scramble versus contest , 1996 .

[12]  Pierre Magal,et al.  Center Manifolds for Semilinear Equations With Non-dense Domain and Applications to Hopf Bifurcation in Age Structured Models , 2009 .

[13]  G. Webb Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[14]  W. Ricker Stock and Recruitment , 1954 .

[15]  S. Ruan,et al.  Sustained oscillations in an evolutionary epidemiological model of influenza A drift , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  Susanna Piazzera,et al.  Asynchronous exponential growth for an age dependent population equation with delayed birth process , 2005 .

[17]  S. Ruan,et al.  On integrated semigroups and age structured models in {$L^p$} spaces , 2007, Differential and Integral Equations.

[18]  Pierre Magal Perturbation of a Globally Stable Steady State and Uniform Persistence , 2009 .

[19]  Pierre Magal,et al.  Hopf bifurcation in a size-structured population dynamic model with random growth , 2009 .

[20]  Y. Kifer Principal eigenvalues, topological pressure, and stochastic stability of equilibrium states , 1990 .

[21]  Susanna Piazzera An age‐dependent population equation with delayed birth process , 2004 .

[22]  Linda J. S. Allen,et al.  The effects of vaccination in an age-dependent model for varicella and herpes zoster , 1998, IEEE Trans. Autom. Control..

[23]  G. Greiner A typical Perron-Frobenius theorem with applications to an age-dependent population equation , 1984 .

[24]  A population equation with diffusion , 2004 .