Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales

Song, Qiankun; Zhao, Zhenjiang

doi:10.1016/j.neucom.2015.06.032

Cited by 102 publications

(17 citation statements)

References 29 publications

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“…Some authors argue that a typical time delay called Leakage (or 'forgetting') delay may occur in the negative feedback term of the neural networks model (these terms are variously known as forgetting or leakage terms) and has a great impact on the dynamics of neural networks [19][20][21][22][23][24][25][26][27][28]. For example, time delay in the stabilizing negative feedback term has a tendency to destabilize a system [29], Li et al [30]pointed out that the existence and uniqueness of the equilibrium point are independent of time delays and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Pang

2016

Math Methods in App Sciences

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This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Pang

2016

Math Methods in App Sciences

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“…The condition is less restrictive than the descriptions on both the sigmond activation functions [9,10] and the Lipschitz-type activation functions.…”

Section: Remarkmentioning

confidence: 99%

“…Many exciting research results have been reported recently [9 -13]. As pointed out in [9,10], neural networks with leakage delay is a class of important networks. In [10], the global exponential stability of complex-valued neural networks with leakage delay was investigated with complex-valued linear matrix inequality technique, by establishing a novel stability lemma .…”

Section: Introductionmentioning

confidence: 99%

“…As pointed out in [9,10], neural networks with leakage delay is a class of important networks. In [10], the global exponential stability of complex-valued neural networks with leakage delay was investigated with complex-valued linear matrix inequality technique, by establishing a novel stability lemma . Then, by using stochastic analysis theory and matrix inequalities technique, the exponential stability of a kind of stochastic neural networks with leakage terms are studied in [11].…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis for Stochastic Markovian Jumping Neural Networks with Leakage Delay

Li¹,

Dai²,

Xiao³

et al. 2017

TOEEJ

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Abstract:The stability problem for a class of stochastic neural networks with Markovian jump parameters and leakage delay is addressed in this study. The sufficient condition to ensure an exponentially stable stochastic neural networks system is presented and proven with Lyapunov functional theory, stochastic stability technique and linear matrix inequality method. The effect of leakage delay on the stability of the neural networks system is discussed and numerical examples are provided to show the correctness and effectiveness of the research results .

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“…Many scholars have devoted themselves into the dynamics analysis of neural networks with various types of time delays and many valuable results have been achieved in the existing literature see [18][19][20][21][22][23][24][25][26]. There are three typical types of time delays for incorporating time delays into neural networks: (i) introduce transmission delays into the neural 2 Complexity networks, and consider discrete delays, distributed delays, mixed delays, even state depended delays, or complex delays; (ii) consider the delays in the leakage term; (iii) take into account neutral type delays.…”

Section: Introductionmentioning

confidence: 99%

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Meng

2017

Complexity

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We propose a class of neutral type quaternion-valued neural networks with delays in the leakage term on time scales that can unify the discrete-time and the continuous-time neural networks. In order to avoid the difficulty brought by the noncommutativity of quaternion multiplication, we first decompose the quaternion-valued system into four real-valued systems. Then, by applying the exponential dichotomic theory of linear dynamic equations on time scales, Banach's fixed point theorem, the theory of calculus on time scales, and inequality techniques, we obtain some sufficient conditions on the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new even for both the case of the neural networks governed by differential equations and the case of the neural networks governed by difference equations and show that, under a simple condition, the continuous-time quaternion-valued network and its corresponding discrete-time quaternionvalued network have the same dynamical behavior for the pseudo almost periodicity. Finally, a numerical example is given to illustrate the feasibility of our results.

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Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales

Cited by 102 publications

References 29 publications

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Stability Analysis for Stochastic Markovian Jumping Neural Networks with Leakage Delay

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

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