scholarly journals Dynamics of the Almost Periodic Discrete Mackey–Glass Model

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 333 ◽  
Author(s):  
Zhijian Yao ◽  
Jehad Alzabut ◽  
Debaldev Jana
Keyword(s):  
Numerical Simulations ◽  
Blood Cells ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic ◽  
Discrete Lyapunov Functional ◽  
Glass Model

This paper is concerned with a class of the discrete Mackey–Glass model that describes the process of the production of blood cells. Prior to proceeding to the main results, we prove the boundedness and extinction of its solutions. By means of the contraction mapping principle and under appropriate assumptions, we prove the existence of almost periodic positive solutions. Furthermore and by the implementation of the discrete Lyapunov functional, sufficient conditions are established for the exponential convergence of the almost periodic positive solution. Examples, as well as numerical simulations are illustrated to demonstrate the effectiveness of the theoretical findings of the paper. Our results are new and generalize some previously-reported results in the literature.

Almost periodic solution of Nicholson’s blowflies difference equation with linear harvesting term

2016 ◽  
Vol 09 (04) ◽  
pp. 1650052
Author(s):  
Zhijian Yao
Keyword(s):  
Positive Solution ◽  
Contraction Mapping ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Difference Model ◽  
Discrete Lyapunov Functional ◽  
Linear Harvesting Term

This paper is concerned with Nicholson’s blowflies difference model with linear harvesting term. We obtain sufficient conditions for the existence of an almost periodic positive solution by using contraction mapping principle. The exponential convergence of almost periodic positive solution is derived by discrete Lyapunov functional.

Almost periodic solution of Nicholson's blowflies model with linear harvesting term and impulsive effects

2015 ◽  
Vol 08 (03) ◽  
pp. 1550053
Author(s):  
Zhijian Yao
Keyword(s):  
Fixed Point ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Nicholson’S Blowflies Model ◽  
Linear Harvesting Term

This paper is concerned with impulsive Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional.

GLOBALLY DYNAMICAL BEHAVIORS FOR DISCRETE LASOTA–WAZEWSKA MODEL WITH SEVERAL DELAYS AND ALMOST PERIODIC COEFFICIENTS

2008 ◽  
Vol 01 (01) ◽  
pp. 95-105 ◽  
Author(s):  
XIAO WANG ◽  
ZHIXIANG LI
Keyword(s):  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Dynamical Behaviors ◽  
Several Delays

The present paper gives two methods to obtain the existence and uniqueness of almost periodic solution [Formula: see text] of the following discrete Lasota–Wazewska model [Formula: see text] one is a new fixed point theorem in cone proved by us, the other is contraction mapping principle. In addition, some sufficient conditions are established for global attractivity of [Formula: see text] by constructing Lyapunov functional.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

scholarly journals ALMOST PERIODIC SOLUTIONS OF IMPULSIVE INTEGRO‐DIFFERENTIAL NEURAL NETWORKS

2010 ◽  
Vol 15 (4) ◽  
pp. 505-516 ◽  
Author(s):  
Gani Tr. Stamov ◽  
Jehad O. Alzabut
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Cauchy Matrix ◽  
Bellman’S Inequality

In this paper, sufficient conditions are established for the existence of almost periodic solutions for system of impulsive integro‐differential neural networks. Our approach is based on the estimation of the Cauchy matrix of linear impulsive differential equations. We shall employ the contraction mapping principle as well as Gronwall‐Bellman's inequality to prove our main result. The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia

scholarly journals Stepanov-Like Asymptotical Almost Periodic Functions and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Yongkun Li ◽  
Yaolu Wang ◽  
Jianglian Xiang
Keyword(s):  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Functions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Delay Differential

In this paper, we first study some basic properties of Stepanov-like asymptotical almost periodic functions including the completeness of the space of Stepanov-like asymptotical almost periodic functions. Then, as an application, based on these and the contraction mapping principle, we obtain sufficient conditions for the existence and uniqueness of Stepanov-like asymptotical almost periodic solutions for a class of semilinear delay differential equations.

scholarly journals Almost Periodic Solutions for Wilson-Cowan Type Model with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shasha Xie ◽  
Zhenkun Huang
Keyword(s):  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Neuronal Population ◽  
Contraction Mapping Principle ◽  
Type Model ◽  
Time Varying ◽  
Almost Periodic ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

Wilson-Cowan model of neuronal population with time-varying delays is considered in this paper. Some sufficient conditions for the existence and delay-based exponential stability of a unique almost periodic solution are established. The approaches are based on constructing Lyapunov functionals and the well-known Banach contraction mapping principle. The results are new, easily checkable, and complement existing periodic ones.

scholarly journals Almost Periodic Solution of a Discrete Commensalism System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Rongyu Han
Keyword(s):  
Periodic Solution ◽  
Comparison Theorem ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Discrete Lyapunov Functional ◽  
Globally Attractive

A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

Existence and exponential stability of almost periodic positive solution for host-macroparasite difference model

2016 ◽  
Vol 09 (02) ◽  
pp. 1650028
Author(s):  
Zhijian Yao
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Difference Model

This paper is concerned with a host-macroparasite difference model. By applying the contraction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Lyapunov functional.

EXPONENTIAL CONVERGENCE OF CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

2007 ◽  
Vol 17 (12) ◽  
pp. 4403-4408
Author(s):  
BINGWEN LIU ◽  
ZHAOHUI YUAN
Keyword(s):  
Neural Networks ◽  
Periodic Function ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
All Solutions

In this paper the convergence behavior of delayed cellular neural networks without almost periodic coefficients are considered. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to an almost periodic function, which are new, and also complement previously known results.

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