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.

scholarly journals Permanence of a Discrete Periodic Volterra Model with Mutual Interference and Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Runxin Wu
Keyword(s):  
Difference Equation ◽  
Functional Response ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Volterra Model

This paper discuss a discrete periodic Volterra model with mutual interference and Beddington-DeAngelis functional response. By using the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system. After that,we give an example to show the feasibility of our main result.

THE PERIODIC VOLTERRA MODEL WITH MUTUAL INTERFERENCE AND IMPULSIVE EFFECT

2012 ◽  
Vol 05 (03) ◽  
pp. 1260005 ◽  
Author(s):  
YUJUAN ZHANG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Bifurcation Theory ◽  
Floquet Theory ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Volterra Model ◽  
Impulsive Effect ◽  
Special Cases ◽  
Coexistence State ◽  
Theoretical Results

In this paper, a periodic Volterra model with mutual interference and impulsive effect is proposed and analyzed. By applying the Floquet theory of impulsive differential equation, some conditions are obtained for the linear stability of semi-trivial periodic solution. Some sufficient conditions are also given for the permanence of the system. Further, standard bifurcation theory is used to show the existence of coexistence state which arises near the semi-trivial periodic solution. Finally, theoretical results are confirmed by some special cases of the system.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

scholarly journals Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Wenzhen Gan ◽  
Canrong Tian ◽  
Qunying Zhang ◽  
Zhigui Lin
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Neumann Boundary Condition ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Food Ingestion ◽  
Nonlocal Delay ◽  
Homogeneous Neumann Boundary Condition

This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.

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