Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay
| Autor: | V. V. Akimenko, Roumen Anguelov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Time Factors proliferating and quiescent phases Population Dynamics Population 0211 other engineering and technologies Phase (waves) 02 engineering and technology Models Biological 03 medical and health sciences Control theory Stability theory education lcsh:QH301-705.5 lcsh:Environmental sciences Ecology Evolution Behavior and Systematics Mathematics lcsh:GE1-350 Population Density education.field_of_study 021103 operations research Ecology population outbreaks Mathematical analysis Age-structured model Ode Nonlinear system 030104 developmental biology lcsh:Biology (General) Nonlinear Dynamics Discrete time and continuous time Harmonic Convection–diffusion equation |
| Zdroj: | Journal of Biological Dynamics, Vol 11, Iss 1, Pp 75-101 (2017) |
| ISSN: | 1751-3766 1751-3758 |
| DOI: | 10.1080/17513758.2016.1236988 |
| Popis: | In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse. |
| Databáze: | OpenAIRE |
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