scholarly journals Extinction in Two-Species Nonlinear Discrete Competitive System

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Liqiong Pu ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Zhanshuai Miao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Discrete System ◽  
Sufficient Conditions ◽  
The Other ◽  
Discrete Equation ◽  
Toxic Substances ◽  
Competitive System ◽  
Globally Attractive ◽  
Nonlinear Discrete System

We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.

Extinction in a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls

2015 ◽  
Vol 08 (01) ◽  
pp. 1550012 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Feedback Controls ◽  
Analysis Technique

In this paper, we consider a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka–Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165–178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.

scholarly journals Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

2016 ◽  
Vol 14 (1) ◽  
pp. 1157-1173 ◽  
Author(s):  
Fengde Chen ◽  
Xiaoxing Chen ◽  
Shouying Huang
Keyword(s):  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Volterra Systems ◽  
Appl Math

AbstractA two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

scholarly journals Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Huili Xiang ◽  
Zhuang Fang ◽  
Zuxiong Li ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Competitive System ◽  
Stochastic Boundedness

A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.

scholarly journals Extinction in a Nonautonomous Discrete Lotka-Volterra Competitive System with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Meng Hu ◽  
Jingyuan Wei
Keyword(s):  
Time Delay ◽  
Positive Solution ◽  
Analytical Techniques ◽  
Logistic Equation ◽  
The Other ◽  
Competitive System ◽  
Globally Attractive ◽  
System With Time Delay

This paper is concerned with a nonautonomous discrete Lotka-Volterra competitive system with time delay. By using some analytical techniques, we prove that, under certain conditions, one of the species will be driven to extinction while the other one will be globally attractive with any positive solution of a discrete logistic equation.

Dynamic behavior of a stochastic SIRS model with two viruses

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang ◽  
Zhixia Han
Keyword(s):  
Growth Rate ◽  
Asymptotic Stability ◽  
Global Existence ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Sirs Model ◽  
The Moment ◽  
Disease Free

AbstractTo study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically ultimately bounded and the moment average in time of the positive solution is bounded. Our results mean that the environmental noise suppresses the growth rate of the individuals and drives the disease to extinction under certain conditions. Finally, numerical simulations are given to illustrate our main results.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

2021 ◽  
pp. 2050043
Author(s):  
Jing Fu ◽  
Qixing Han ◽  
Daqing Jiang ◽  
Yanyan Yang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Necessary Conditions ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Interacting Species ◽  
Sufficient And Necessary Conditions ◽  
Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

A stochastic vaccinated epidemic model incorporating Lévy processes with a general awareness-induced incidence

2021 ◽  
pp. 2150044
Author(s):  
Khadija Akdim ◽  
Adil Ez-Zetouni ◽  
Mehdi Zahid
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Dynamic Behavior ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Global Positive Solution ◽  
Levy Noise ◽  
Disease Free

In this paper, we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Lévy noise. First, we show that this model has a unique global positive solution. Therefore, we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points. Furthermore, when [Formula: see text], we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Lévy noise is null. Finally, we present some examples to illustrate the analytical results by numerical simulations.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Coexistence for a kind of stochastic three-species competitive models

2019 ◽  
Vol 17 (1) ◽  
pp. 1203-1219
Author(s):  
Nantian Huang ◽  
Jiabing Huang ◽  
Yuming Wei ◽  
Yongjian Liu
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Convergence In Distribution ◽  
Threshold Values ◽  
Linear Diffusion ◽  
Ecological Balance ◽  
Non Linear ◽  
Competitive Model ◽  
Theoretical Results

Abstract The coexistence of species sustains the ecological balance in nature. This paper focuses on sufficient conditions for the coexistence of a three-species stochastic competitive model, where the model has non-linear diffusion parts. Three values λ3z, λ3x and λ3y are introduced and calculated from the coefficients, which can be considered as threshold values. Moreover, convergence in distribution of the positive solution of the model is also addressed. A few numerical simulations are carried out to illustrate the theoretical results.

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