Stability analysis for a size-structured model of species in a space-limited habitat

2016 ◽  
Vol 09 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Ze-Rong He ◽  
Qiang-Jun Xie ◽  
Hai-Tao Wang
Keyword(s):  
Population Model ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Reproduction Rate ◽  
Structured Population Model ◽  
Structured Model ◽  
Basic Reproduction Rate ◽  
Structured Population ◽  
State And Local ◽  
The Stability

We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations are presented to illustrate the obtained results.

scholarly journals The solution and the stability of a nonlinear age-structured population model

2003 ◽  
Vol 45 (2) ◽  
pp. 153-165 ◽  
Author(s):  
Norhayati ◽  
G. C. Wake
Keyword(s):  
Population Model ◽  
Initial Conditions ◽  
Age Distribution ◽  
Initial Population ◽  
Illustrative Case ◽  
Structured Population Model ◽  
Structured Population ◽  
Age Structured ◽  
The Stability ◽  
Age Structured Population

AbstractWe consider an age-structured population model achieved by modifying the classical Sharpe-Lotka-McKendrick model, incorporating an overcrowding effect or competition for resources term. This term depends on the whole population rather than on any specific age group, in the case of overcrowding or limitation of resources. We investigate the solutions for arbitrary initial conditions. We consider the existence of a steady age distribution and its stability and are able to determine this for a simple illustrative case. If the non-trivial steady age distribution is unstable, there is a critical initial population size beyond which the population explodes. This watershed is independent of the shape of the initial age distribution.

scholarly journals Modelling of a One-Sex Age-Structured Population Dynamics with Child Care

2007 ◽  
Vol 12 (1) ◽  
pp. 77-94 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Child Care ◽  
Parental Care ◽  
Population Model ◽  
Population Based ◽  
Structured Population Model ◽  
Structured Population ◽  
Structured Population Dynamics ◽  
Age Structured ◽  
The Stability ◽  
Age Structured Population

The Sharpe-Lotka-Mckendrick-von Foerster one-sex population model and Fredrickson-Hoppensteadt-Staroverov two-sex population one are well known in mathematical biology. But they do not describe dynamics of populations with child care. In recent years some models were proposed to describe dynamics of the wild population with child care. Some of them are based on the notion of the density of offsprings under maternal (or parental) care. However, such models do not ensure the fact that offsprings under maternal (or parental) care move together with their mothers (or both parents). In recent years to solve this problem, some models of a sex-age-structured population, based on the discrete set of newborns, were proposed and examined analytically. Numerical schemes for solving of a one-sex age-structured population model with and without spatial dispersal taking into account a discrete set of offsprings and child care are proposed and results are discussed in this paper. The model consists of partial integrodifferential equations subject to conditions of the integral type. Numerical experiments exhibit the stability of the separable solutions to these models.

scholarly journals On the linearized stability of age-structured multispecies populations

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
Jozsef Z. Farkas
Keyword(s):  
Population Model ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Structured Population Model ◽  
Interacting Species ◽  
Structured Population ◽  
Linearized Stability ◽  
Age Structured ◽  
The Stability ◽  
Age Structured Population

We consider a general nonlinear age-structured population model withninteracting species. We deduce the characteristic function in the form of a determinant of ann-by-nmatrix. Then we formulate some biologically meaningful sufficient conditions for the stability (resp., instability) of positive stationary solutions of the system.

scholarly journals Dynamics of the Stage Structured Population Model, Predator Accompanied by Michaelis Menten Holling Type Functional Responseand Delay and Prey Taking Refuge

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
N. Mohana Sorubha Sundari, Et. al.
Keyword(s):  
Population Model ◽  
Local Stability ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Structured Population Model ◽  
Predator Prey ◽  
Structured Population ◽  
Prey System ◽  
Two Stages

The current work considers predator prey system, prey taking refuge, predator reckoned with time delay and Michaelis Menten Holling type II response function undergoing two stages: juvenile and mature. From the characteristic equation, we derive conditions for the local stability of the system at the equilibrium points. Also, at the coexistence equilibrium point, the system is analyzed for the occurrence of Hopf bifurcation. Lyapunov function provides sufficient conditions for the global stability of the system. Numerical simulations are given to support the theory.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

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