Hopf Bifurcation in an Age-structured Population Model with Two Delays
نویسندگان
چکیده
This paper is devoted to the study of an age-structured population system with Riker type birth function. Two time lag factors is considered for the model. One time lies in the birth process and the another is in the birth function. We investigate some dynamical properties of the equation by using integrated semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system. The obtained results show how the two delays affect these dynamical properties.
منابع مشابه
Hopf Bifurcation for a Spatially and Age Structured Population Dynamics Model
This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indi...
متن کاملDynamics of an eco-epidemic model with stage structure for predator
The predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. The intraspecific competition of infected prey is considered. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibriu...
متن کاملBifurcation Analysis of a Stage-Structured Prey-Predator System with Discrete and Continuous Delays
A three-stage-structured prey-predator model with discrete and continuous time delays is studied. The characteristic equations and the stability of the boundary and positive equilibrium are analyzed. The conditions for the positive equilibrium occurring Hopf bifurcation are given, by applying the theorem of Hopf bifurcation. Finally, numerical simulation and brief conclusion are given.
متن کاملStability and HOPF Bifurcation Analysis in a Stage-structured Predator-prey system with Two Time Delays
A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...
متن کاملA THREE DIMENSIONAL HTLV-1 MODEL WITH INTRACELLULAR AND IMMUNE ACTIVATION DELAYS
In this paper, a three dimensional mathematical model for HTLV-1infection with intracellular delay and immune activation delay is investigated.By applying the frequency domain approach, we show that time delays candestabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and sta-ble or unstable periodic oscillations. At the end, numerical simulations areillustrated.
متن کامل