scholarly journals Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongwu Zheng ◽  
Fengqin Zhang ◽  
Jianquan Li
Keyword(s):  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Positive Equilibrium ◽  
Stability Switch ◽  
Birth Function ◽  
Maturation Delay ◽  
Trivial Equilibrium ◽  
Species Population ◽  
Single Species Population

A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.

scholarly journals Comparison principles for impulsive parabolic equations with applications to models of single species growth

1991 ◽  
Vol 32 (4) ◽  
pp. 382-400 ◽  
Author(s):  
L. H. Erbe ◽  
H. I. Freedman ◽  
X. Z. Liu ◽  
J. H. Wu
Keyword(s):  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Single Species ◽  
Reaction Diffusion Equation ◽  
Equation Modeling ◽  
Positive Equilibrium ◽  
Comparison Principles ◽  
Nonlinear Parabolic ◽  
Species Population ◽  
Single Species Population

AbstractThis paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

Survival analysis of a stochastic single-species population model with jumps in a polluted environment

2015 ◽  
Vol 09 (01) ◽  
pp. 1650011 ◽  
Author(s):  
Meng Liu ◽  
Ke Wang
Keyword(s):  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Polluted Environment ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Species Population ◽  
The Mean ◽  
Single Species Population ◽  
Lévy Jumps

This paper is concerned with a stochastic single-species system with Lévy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean, stability in the mean and stochastic permanence are obtained. The threshold between extinction and weak persistence in the mean is established. At the same time, under a simple condition, it is proved that this threshold also is the threshold between extinction and stability in the mean. The results reveal that Lévy jumps have significant effects to the persistence and extinction results.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

scholarly journals Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ronghua Tan ◽  
Zuxiong Li ◽  
Shengliang Guo ◽  
Zhijun Liu
Keyword(s):  
Lyapunov Functions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Single Species ◽  
Different Types ◽  
Species Population ◽  
Impulsive Perturbations ◽  
Single Species Population ◽  
Single Species Model

This is a continuation of the work of Tan et al. (2012). In this paper a periodic single species model controlled by constant impulsive perturbation is investigated. The constant impulse is realized at fixed moments of time. With the help of the comparison theorem of impulsive differential equations and Lyapunov functions, sufficient conditions for the permanence and global attractivity are established, respectively. Also, by comparing the above results with corresponding known results of Tan et al. (2012) (i.e., the above model with linear impulsive perturbations), we find that the two different types of impulsive perturbations have influence on the above dynamics. Numerical simulations are presented to substantiate our analytical results.

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