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Xiangyun Shi,Xueyong Zhou,Xinyu Song 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.. In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings..
Shi, Xiangyun,Zhou, Xueyong,Song, Xinyu The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.
Zhang, Zhengqiu,Zhou, Zheng Korean Mathematical Society 2011 대한수학회지 Vol.48 No.2
In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.
PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY
MAROUN MARIETTE R.,RAFFOUL YOUSSEF N. Korean Mathematical Society 2005 대한수학회지 Vol.42 No.2
We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.
PSEUDO ALMOST PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS INVOLVING REFLECTION OF THE ARGUMENT
Piao, Daxiong Korean Mathematical Society 2004 대한수학회지 Vol.41 No.4
In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.
QUALITATIVE ANALYSIS OF A GENERAL PERIODIC SYSTEM
Xu, Shihe Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.
Periodic Solutions of a System of Piecewise Linear Difference Equations
Tikjha, Wirot,Lapierre, Evelina Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.2
In this article we consider the following system of piecewise linear difference equations: x<sub>n+1</sub> = |x<sub>n</sub>| - y<sub>n</sub> - 1 and y<sub>n+1</sub> = x<sub>n</sub> + |y<sub>n</sub>| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.
Zeng, Zhijun Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.3
With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.
Dai, Binxiang,Zou, Jiezhong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.
POSITIVE PERIODIC SOLUTIONS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS
LIU, YUJI,XIA, JIANYE,GE, WEIGAO 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.