IMPULSIVE DISPERSAL OF PLANT SEEDS IN SINGLE SPECIES MODEL

2007 ◽  
Vol 15 (03) ◽  
pp. 385-396
Author(s):  
LIMIN WANG ◽  
YUANSHUN TAN ◽  
LANSUN CHEN
Keyword(s):  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Plant Seeds ◽  
Impulsive Diffusion ◽  
Globally Stable ◽  
Natural Description ◽  
Negative Growth ◽  
Single Species Model

In this paper, a single species model with impulsive diffusion between two patches is proposed, which provides a more natural description of plant seeds dynamics compared with the continuous or discrete ones. By using the discrete dynamical system generated by a monotone, concave map for the dispersal model and a ∊1 - ∊2 variation, it is proved that the Poincare map has a globally stable positive fixed point. This implies that the system considered here has a globally stable positive periodic solution under some sufficient conditions. Further numerical simulations show that the diffusion can save the extinction though the species has a negative growth rate in one patch.

scholarly journals Analysis of a Single Species Model with Dissymmetric Bidirectional Impulsive Diffusion and Dispersal Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Haiyun Wan ◽  
Long Zhang ◽  
Zhidong Teng
Keyword(s):  
Population Dynamics ◽  
Periodic Solution ◽  
Global Stability ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Migration Behavior ◽  
Natural Ecosystem ◽  
Impulsive Diffusion ◽  
Theoretical Results ◽  
Single Species Model

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in the real natural ecosystem, impulsive diffusion provides a more suitable manner to model the actual dispersal (or migration) behavior for many ecological species. In addition, the species not only requires some time to disperse or migrate among the patches but also has some possibility of loss during dispersal. In view of these facts, a single species model with dissymmetric bidirectional impulsive diffusion and dispersal delay is formulated. Criteria on the permanence and extinction of species are established. Furthermore, the realistic conditions for the existence, uniqueness, and the global stability of the positive periodic solution are obtained. Finally, numerical simulations and discussion are presented to illustrate our theoretical results.

Permanence and extinction of a single species model in polluted environment

2020 ◽  
Vol 13 (04) ◽  
pp. 2050031
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Logistic Equation ◽  
Polluted Environment ◽  
Math Model ◽  
Generalized Logistic Equation ◽  
Appl Math ◽  
Single Species Model

Under the assumption that the growth of the population satisfies the generalized logistic equation, a new single species model in polluted environment is proposed in this work. Sufficient conditions for permanence and extinction of the species in the model are given respectively. It is shown that our model and the results are improvements of those in He and Wang [Appl. Math. Model. 31 (2007) 2227–2238].

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.

scholarly journals An Impulsive Periodic Single-Species Logistic System with Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Chenxue Yang ◽  
Mao Ye ◽  
Zijian Liu
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Patchy Environment ◽  
Estimation Technique ◽  
Numerical Examples ◽  
Integrable Form

We study a single-species periodic logistic type dispersal system in a patchy environment with impulses. On the basis of inequality estimation technique, sufficient conditions of integrable form for the permanence and extinction of the system are obtained. By constructing an appropriate Lyapunov function, conditions for the existence of a unique globally attractively positive periodic solution are also established. Numerical examples are shown to verify the validity of our results and to further discuss the model.

scholarly journals A Single Species Model with Symmetric Bidirectional Impulsive Diffusion and Dispersal Delay

2012 ◽  
Vol 03 (09) ◽  
pp. 1079-1088 ◽  
Author(s):  
Haiyun Wan ◽  
Long Zhang ◽  
Hongli Li
Keyword(s):  
Single Species ◽  
Impulsive Diffusion ◽  
Single Species Model

PERMANENCE AND UNIFORMLY ASYMPTOTICAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR A SINGLE-SPECIES MODEL WITH FEEDBACK CONTROL ON TIME SCALES

2014 ◽  
Vol 07 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang ◽  
Hongtao Zhang
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Single Species ◽  
Asymptotical Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniformly Asymptotical Stability ◽  
Single Species Model

In this paper, using the time scale calculus theory, we first discuss the permanence of a single-species model with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. Moreover, we present an illustrative example to show the effectiveness of obtained results.

scholarly journals Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Lingzhi Huang ◽  
Zhichun Yang
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Comparison Theorem ◽  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model ◽  
Impulsive Diffusion

We consider a delayed predator-prey model with harvesting effort and impulsive diffusion between two patches. By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. Furthermore, the permanence of the system is derived. The obtained results will modify and improve the ones in some existing publications and give the estimate for the ultimately low and upper boundedness of the systems.

scholarly journals Permanence and Periodic Solutions for a Two-Patch Impulsive Migration PeriodicN-Species Lotka-Volterra Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Analysis Method ◽  
Competitive System ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Globally Stable

We study a two-patch impulsive migration periodicN-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.

scholarly journals Dynamics of a stochastic population model with predation effects in polluted environments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Guanghai Song
Keyword(s):  
Numerical Simulations ◽  
Growth Rates ◽  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Polluted Environment ◽  
Predation Effect ◽  
Predation Effects ◽  
Stochastic Population Model ◽  
Single Species Model

AbstractThe present paper puts forward and probes a stochastic single-species model with predation effect in a polluted environment. We propose a threshold between extermination and weak persistence of the species and provide sufficient conditions for the stochastic persistence of the species. In addition, we evaluate the growth rates of the solution. Theoretical findings are expounded by some numerical simulations.

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