Global Exponential Stability and Periodic Solutions of FCNNs with Constant Delays and Time-Varying Delays

2009 ◽  
Author(s):  
Qianhong Zhang ◽  
Wei Luo
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Time Varying

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 Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is 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>

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