Long-Time Behavior of Spatially and Size-Structured Population Dynamics with Delayed Birth Process

2017 ◽  
Vol 27 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Dongxue Yan ◽  
Xianlong Fu
Keyword(s):  
Population Dynamics ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Time Behavior ◽  
Birth Process ◽  
Structured Population ◽  
Population Dynamics Model ◽  
Structured Population Dynamics ◽  
Long Time ◽  
Asynchronous Exponential Growth

This paper is devoted to the study of a spatially and size-structured population dynamics model with delay in the birth process. We investigate some dynamical properties of the equation by using [Formula: see text]-semigroup theory and spectral analysis arguments, through which we obtain some sufficient conditions of asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. Some examples are presented and simulated to illustrate the obtained results.

scholarly journals A One-Sex Population Dynamics Model with Discrete Set of Offsprings and Child Care

2008 ◽  
Vol 13 (4) ◽  
pp. 525-552
Author(s):  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Child Care ◽  
Maternal Care ◽  
Deterministic Model ◽  
Large Time Behavior ◽  
Reproductive Age ◽  
Time Behavior ◽  
Care Groups ◽  
Population Dynamics Model ◽  
Long Time

We present a one-sex age-structured population dynamics deterministic model with a discrete set of offsprings, child care, environmental pressure, and spatial migration. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Individuals of reproductive age are divided into fertile single and taking child care groups. All individuals of pre-reproductive age are divided into young (under maternal care) and juvenile (offspring who can live without maternal care) classes. It is assumed that all young offsprings move together with their mother and that after the death of mother all her young offsprings are killed. The model consists of integro-partial differential equations subject to the conditions of the integral type. Number of these equations depends on a biologically possible maximal newborns number of the same generation produced by an individual. The existence and uniqueness theorem is proved, separable solutions are studied, and the long time behavior is examined for the solution with general type of initial distributions in the case of non-dispersing population. Separable and more general (nonseparable) solutions, their large time behavior, and steady-state solutions are studied for the population with spatial dispersal, too.

Sign in / Sign up

Export Citation Format

Share Document