scholarly journals Global Exponential Stability of Positive Almost Periodic Solutions for a Fishing Model with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hong Zhang ◽  
Shuhua Gong ◽  
Jianying Shao
Keyword(s):  
Numerical Simulation ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Positive Almost Periodic Solutions

This paper is concerned with a nonautonomous fishing model with a time-varying delay. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive almost periodic solutions of the model with almost periodic coefficients and delays. Moreover, an example and its numerical simulation are given to illustrate the main results.

scholarly journals Global Exponential Stability of Positive Almost Periodic Solutions for a Delay Logarithmic Population Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Wei Chen ◽  
Wentao Wang
Keyword(s):  
Numerical Simulation ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Population Model ◽  
Global Exponential Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Almost Periodic Solutions

This paper is concerned with a delay logarithmic population model. Under proper conditions, we employ a novel proof to establish a criterion on guaranteeing the existence and global exponential stability of positive almost periodic solutions for the model. Moreover, an example and its numerical simulation are given to illustrate the main results.

scholarly journals Existence and Global Exponential Stability of Almost Periodic Solutions for SICNNs with Nonlinear Behaved Functions and Mixed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao ◽  
Chuangxia Huang ◽  
Yao Long
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Techniques

By using the Leray-Schauder fixed point theorem and differential inequality techniques, several new sufficient conditions are obtained for the existence and global exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with discrete and distributed delays. The model in this paper possesses two characters: nonlinear behaved functions and all coefficients are time varying. Hence, our model is general and applicable to many known models. Moreover, our main results are also general and can be easily deduced to many simple cases, including some existing results. An example and its simulation are employed to illustrate our feasible results.

scholarly journals Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays

2021 ◽  
Vol 7 (3) ◽  
pp. 3653-3679
Author(s):  
Nina Huo ◽  
◽  
Bing Li ◽  
Yongkun Li ◽  
◽  
...  
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic

<abstract><p>In this paper, we consider a class of Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays whose coefficients are Clifford numbers except the time delays. Based on the Banach fixed point theorem and inequality techniques, we obtain the existence and global exponential stability of almost periodic solutions in distribution of this class of neural networks. Even if the considered neural networks degenerate into real-valued, complex-valued and quaternion-valued ones, our results are new. Finally, we use a numerical example and its computer simulation to illustrate the validity and feasibility of our theoretical results.</p></abstract>

scholarly journals Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNNs with Time-Varying Leakage Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Wentao Wang ◽  
Bingwen Liu
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Functional Method ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper is concerned with the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage (or forgetting) terms. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of pseudo almost periodic solutions by using Lyapunov functional method and differential inequality techniques. We also provide numerical simulations to support the theoretical result.

scholarly journals Existence and Global Exponential Stability of Almost Periodic Solutions for a Class of Delay Duffing Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Li Yang ◽  
Yongkun Li
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Duffing Equations ◽  
Linear Dynamic

Based on the exponential dichotomy of linear dynamic equations on time scales, we obtain some sufficient conditions for the existence and global exponential stability of almost periodic solutions for a class of Duffing equations with time-varying delays on time scales. We also present numerical examples to show the feasibility of obtained results. The results of this paper are completely new even when the time scaleT=RorZand are complementary to the previously known results.

Sign in / Sign up

Export Citation Format

Share Document