scholarly journals Extinction and permanence in nonautonomous competitive system with stage structure

2002 ◽  
Vol 274 (2) ◽  
pp. 667-684 ◽  
Author(s):  
Shengqiang Liu ◽  
Lansun Chen ◽  
Zhuojun Liu
Keyword(s):  
Stage Structure ◽  
Competitive System

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 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.

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].

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.

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