scholarly journals Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Junxia Meng
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Multiple Time ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper presents a new generalized model of hematopoiesis with multiple time-varying delays. The main purpose of this paper is to study the existence and the global exponential stability of the positive pseudo almost periodic solutions, which are more general and complicated than periodic and almost periodic solutions. Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. These results improve and extend some known relevant results.

scholarly journals Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Lili Zhao ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Distributed Delays ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

Some sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of weighted pseudo-almost periodic solutions to a class of neutral type high-order Hopfield neural networks with distributed delays by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results. Moreover, an example is given to show the effectiveness of the proposed method and results.

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 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 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.

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