GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS OF HIGH-ORDER HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED DELAYS OF NEUTRAL TYPE

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.

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

AIMS Mathematics ◽

10.3934/math.2022202 ◽

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

Mathematics ◽

10.3390/math7040321 ◽

2019 ◽

Vol 7 (4) ◽

pp. 321 ◽

Cited By ~ 1

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.

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