scholarly journals Extinction of a two species competitive stage-structured system with the effect of toxic substance and harvesting

2019 ◽  
Vol 17 (1) ◽  
pp. 856-873 ◽  
Author(s):  
Xiaoyan Huang ◽  
Fengde Chen ◽  
Xiangdong Xie ◽  
Liang Zhao
Keyword(s):  
Toxic Substance ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Volterra Model ◽  
Toxic Substances ◽  
Competitive System ◽  
Structured System ◽  
Extinction Property ◽  
Appl Math

Abstract The extinction property of a two species competitive stage-structured phytoplankton system with harvesting is studied in this paper. Several sets of sufficient conditions which ensure that one of the components will be driven to extinction are established. Our results supplement and complement the results of Li and Chen [Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances, J. Comput. Appl. Math., 2009, 231(1), 143-153] and Liu, Chen, Luo et al. [Extinction and permanence in nonautonomous competitive system with stage structure, J. Math. Anal. Appl., 2002, 274(2), 667-684].

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 Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Yuanke Li
Keyword(s):  
Global Stability ◽  
Toxic Effect ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Competitive System ◽  
Comparison Arguments ◽  
Double Time

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

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.

scholarly journals Existence and Global Attractivity of Positive Periodic Solutions for a Two-Species Competitive System with Stage Structure and Impulse

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Changjin Xu ◽  
Daxue Chen
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Competitive System

A class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained 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 Dynamic Behaviors of a Nonautonomous Impulsive Competitive System with the Effect of Toxic Substance

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen ◽  
Liujuan Chen
Keyword(s):  
Global Attractivity ◽  
Toxic Substance ◽  
The Other ◽  
Sufficient Condition ◽  
Toxic Substances ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Paper Supplement

We firstly propose a nonautonomous impulsive Lotka-Volterra competitive system with the effect of toxic substance. Only one of the two species could produce toxic substance. Sufficient condition which guarantees the extinction of one of the species and the global attractivity of the other species is obtained. We also present an example to verify our main results, which show that species still is possibly driven to extinction when only one of the two species produces toxic substances. The results of this paper supplement the existing results.

scholarly journals The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 173 ◽  
Author(s):  
Liang Zhao ◽  
Fengde Chen ◽  
Saixi Song ◽  
Guizhen Xuan
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Crucial Role ◽  
Sufficient Conditions ◽  
Toxic Substances ◽  
Competitive System ◽  
Feedback Controls

A non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one of the species by using some suitable Lyapunov type extinction function. Our analyses extend those of Xie et al. (Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton. Advances in Difference Equations, 2016, 2016, 258) and show that the feedback controls and toxic substances have no effect on the permanence of the system but play a crucial role on the extinction of the system. Some known results are extended.

A non-autonomous competitive system with stage structure and distributed delays

2010 ◽  
Vol 140 (5) ◽  
pp. 1061-1080 ◽  
Author(s):  
Jiaoyan Wang ◽  
Zhaosheng Feng
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Functional Responses ◽  
Competitive System ◽  
Competitive Model ◽  
Distributed Time Delay

AbstractWe consider a non-autonomous competitive model with generalized functional responses for interaction among n species, the adult members of which are in competition. For each of the n species the model incorporates a distributed time delay which represents the time from birth to maturity of that species. Based on some comparison arguments, we discuss the permanence and extinction of the species. By virtue of the continuation theorem of coincidence degree theory, we prove the existence of a positive periodic solution. By means of constructing appropriate Lyapunov functionals, we obtain sufficient conditions for the uniqueness and the global stability of the periodic solution. Two examples are given to illustrate the feasibility of our main results.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Permanence of a Discrete Periodic Volterra Model with Mutual Interference

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Lijuan Chen ◽  
Liujuan Chen
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Volterra Model

This paper discusses a discrete periodic Volterra model with mutual interference and Holling II type functional response. Firstly, sufficient conditions are obtained for the permanence of the system. After that, we give an example to show the feasibility of our main results.

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