scholarly journals Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ahmadjan Muhammadhaji ◽  
Azhar Halik
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Periodic Solutions ◽  
Population Model ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Spruce Budworm ◽  
Positive Periodic Solutions ◽  
Inequality Techniques

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

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.

scholarly journals Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Zhenguo Luo ◽  
Jianhua Huang ◽  
Liping Luo ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Population Model ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Contractive Operator ◽  
Inequality Techniques

Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

scholarly journals Permanence and Global Attractivity of a Discrete Two-Prey One-Predator Model with Infinite Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Zhixiang Yu ◽  
Zhong Li
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Predator Model

A discrete two-prey one-predator model with infinite delay is proposed. A set of sufficient conditions which guarantee the permanence of the system is obtained. By constructing a suitable Lyapunov functional, we also obtain sufficient conditions ensuring the global attractivity of the system. An example together with its numerical simulation shows the feasibility of the main results.

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

scholarly journals Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo
Keyword(s):  
Feedback Control ◽  
Population Model ◽  
Contraction Mapping ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Contraction Mapping Principle ◽  
Positive Periodic Solutions ◽  
Special Cases ◽  
Existence And Stability ◽  
Inequality Techniques

We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.

scholarly journals Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Zhi-Long Jin
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Positive Periodic Solutions ◽  
Liapunov Functionals ◽  
Delay Differential System ◽  
Several Delays ◽  
Delay Differential

By constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback controldy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))),du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation with several delays and feedback control, some new results are obtained.

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 Global Attractivity of Positive Periodic Solution for a Delayed Predator-Prey System with Diffusion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yuanfu Shao ◽  
Xiaolan Xie ◽  
Zhixiang Ju
Keyword(s):  
Periodic Solution ◽  
Numerical Analysis ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

By constructing a suitable Lyapunov functional, the global attractivity of positive periodic solutions for a delayed predator-prey system with diffusion and impulses is studied in this paper. Finally, an example and numerical analysis are given to show the effectiveness of the main results.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL POPULATION MODEL WITH DELAYS

2008 ◽  
Vol 01 (01) ◽  
pp. 107-120 ◽  
Author(s):  
QI WANG ◽  
BINXIANG DAI
Keyword(s):  
Periodic Solutions ◽  
Population Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solutions ◽  
Analysis Techniques ◽  
Contractive Operator

In this paper, by using the theory of abstract continuous theorem of k-set contractive operator and some analysis techniques, we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model.

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