On the Existence of Positive Periodic Solutions for N-Species Lotka-Volterra Competitive Systems with Distributed Delays and Impulses

2021 ◽  
Author(s):  
Mimia Benhadri ◽  
Tomás Caraballo
Keyword(s):  
Periodic Solutions ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Competitive Systems

scholarly journals Existence of Positive Periodic Solutions for Periodic Neutral Lotka-Volterra System with Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Volterra System

By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays:xi′(t)=xi(t)[ri(t)-∑j=1naij(t)xj(t)-∑j=1n‍bij(t)∫-τij0‍fij(ξ)xj(t+ξ)dξ-∑j=1n‍cij(t)∫-σij0‍gij(ξ)xj′(t+ξ)dξ],  Δxi(tk)=-Iik(xi(tk)),  i=1,2,…,n,  k=1,2,….Some verifiable criteria are established easily.

scholarly journals Periodic solutions of periodic generalized food limited model

2001 ◽  
Vol 25 (4) ◽  
pp. 265-271 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Distributed Delays ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
State Dependent

By using the continuation theorem of coincidence degree theory, the existence of positive periodic solutions for a periodic generalized food limited model with state dependent delays and distributed delays is studied, respectively.

scholarly journals Global Positive Periodic Solutions for Periodic Two-Species Competitive Systems with Multiple Delays and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Yunhui Zeng
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Positive Periodic Solutions ◽  
Analysis Techniques ◽  
Competitive Systems ◽  
Sufficiency Theorems

A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses, by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

scholarly journals Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Rouzimaimaiti Mahemuti ◽  
Zhidong Teng
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Competitive Systems ◽  
Volterra Systems ◽  
Special Cases

We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

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