PERMANENCE AND UNIFORMLY ASYMPTOTICAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR A SINGLE-SPECIES MODEL WITH FEEDBACK CONTROL ON TIME SCALES

2014 ◽  
Vol 07 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang ◽  
Hongtao Zhang
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Single Species ◽  
Asymptotical Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniformly Asymptotical Stability ◽  
Single Species Model

In this paper, using the time scale calculus theory, we first discuss the permanence of a single-species model with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. Moreover, we present an illustrative example to show the effectiveness of obtained results.

scholarly journals The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 321 ◽  
Author(s):  
Bing Li ◽  
Yongkun Li ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

scholarly journals C1-Almost Periodic Solutions of BAM Neural Networks with Time-Varying Delays on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yongkun Li ◽  
Lili Zhao ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
New Type ◽  
Inequality Techniques

On a new type of almost periodic time scales, a class of BAM neural networks is considered. By employing a fixed point theorem and differential inequality techniques, some sufficient conditions ensuring the existence and global exponential stability ofC1-almost periodic solutions for this class of networks with time-varying delays are established. Two examples are given to show the effectiveness of the proposed method and results.

scholarly journals Almost Periodic Solutions for Neutral-Type BAM Neural Networks with Delays on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scales ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bam Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Linear Dynamic ◽  
Dynamical Behaviors

Using the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and exponential stability of almost periodic solutions for a class of neutral-type BAM neural networks with delays on time scales. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new even if the time scale𝕋=ℝorℤand complementary to the previously known results.

Existence and Global Exponential Stability of Almost Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Distributed Leakage Delays on Time Scales

2016 ◽  
Vol 13 (10) ◽  
pp. 7054-7065
Author(s):  
Changjin Xu ◽  
Xiaofei Li ◽  
Songbo Hu ◽  
Haitao Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Linear Differential

In this paper, we deal with a class of shunting inhibitory cellular neural networks (SICNNs) with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of SICNNs are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies.

EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR NICHOLSON'S BLOWFLIES MODELS WITH PATCH STRUCTURE AND LINEAR HARVESTING TERMS OB TIME SCALES

2012 ◽  
Vol 05 (03) ◽  
pp. 1250038 ◽  
Author(s):  
Yongkun Li ◽  
Li Yang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Patch Structure ◽  
Time Scale Calculus ◽  
Lyapunov Function Method ◽  
Existence And Stability

In this paper, by constructing a contraction mapping and using the time scale calculus theory and the Lyapunov function method, we obtain some sufficient conditions for the existence and stability of almost periodic solutions for a class of Nicholson's blowflies models with patch structure and linear harvesting terms on time scales. The results of this paper are completely new. Moreover, we present an illustrative example and numerical simulation to show the effectiveness of obtained results.

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.

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