Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term

Li, Ruoxia; Cao, Jinde

doi:10.1016/j.amc.2016.01.016

Cited by 101 publications

(48 citation statements)

References 33 publications

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“…Recently, the stability of systems with leakage delays has become one of the hot topics . A typical time delay called as leakage delay may exist in the negative feedback terms of the system, and it has a great impact on the dynamic behaviors of the neural networks, such as on the instability or poor system performance of neural networks.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

Arbi

2017

Math Methods in App Sciences

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Bidirectional associative memory models are 2‐layer heteroassociative networks. In this work, we prove the existence and the global exponential stability of the unique weighted pseudo–almost periodic solution of bidirectional associative memory neural networks with mixed time‐varying delays and leakage time‐varying delays on time‐space scales. Some sufficient conditions are given for the existence, the convergence, and the global exponential stability of the weighted pseudo–almost periodic solution by using fixed‐point theorem and differential inequality techniques. The results of this paper complement the previous outcomes. An example is given to show the effectiveness of the derived results via computer simulations.

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Section: Introductionmentioning

confidence: 99%

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

Arbi

2017

Math Methods in App Sciences

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“…Since [26], it is more important and necessary to investigate the stability of delayed NNs including leakage effects. For this purpose, recently relevant leakage problems had arisen, and significant progress has been made (see, e.g., [27][28][29]. Recently, in [27], the global exponential stability for BAM neural networks with time-varying leakage delays was discussed, which extended and improved the main results developed in [25,26].…”

Section: Introductionmentioning

confidence: 69%

“…However, in practical world, the time-varying delay may be an interval delay, that is, the lower bound of the delay interval is not restricted to zero. For this case, the stability criteria for dynamical systems proposed in [29,30] cannot be applied because those results could not consider the case where lower bound of delay is nonzero. Therefore, it is of significant importance to study the stability of NNs containing a nonzero lower bound of the interval time-varying delays, and some of the researchers have reported fruitful results in the previous literature (see [8][9][10][11][12][13]16]).…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent stability criteria for neutral-type neural networks with interval time-varying delay signals under the effects of leakage delay

et al. 2018

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We examine the stability problem for delayed neutral-type neural networks (NNs) with interval time-varying delay signals under the effects of leakage term by constructing a suitable Lyapunov-Krasovskii functionals (LKFs) with the triple-and four-integral terms and using the famous Jensen inequality, Wirtinger single integral inequality (WSII), and Wirtinger double integral inequality (WDII), combined with the reciprocally convex approach (RCC) for the stability of addressing NNs. Therefore, the major contribution of this study lies in a consideration of new integral inequalities and improved LKFs, fully taking the relationship between the terms in the Leibniz-Newton formula within the framework of linear matrix inequalities (LMIs). Moreover, we assume that the lower bound of interval time-varying delay is not restricted to zero. Using several examples, we show that the proposed stability criterion is less conservative than previous results. Also, the proposed technique is applied to benchmark problem that is associated with reasonable issues to showing feasibility on a real-world problem, including transporting time delay signals and leakage delay as a process variable in the quadruple-tank process system.

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“…To the best of our knowledge, the fractional-order complex-valued one has not been investigated yet in the existing literature. Inspired by the above discussion, based on the works in [30][31][32][33][34][35], in this paper we pay attention to the stability analysis of delayed fractional-order complex-valued memristive neural networks. By means of appropriate Lyapunov functional, nonlinear measure method as well as inequality techniques, some sufficient conditions are shown to ascertain the existence, uniqueness and stability of the equilibrium point for the given fractional order complex-valued systems.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays

Wei

Chen

et al. 2016

Neural Process Lett

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This paper presents a theoretical results on the existence, uniqueness of equilibrium point for a class of fractional order complex-valued delayed memristive neural networks, subsequently, its stability analysis are also considered. In a complex-valued recurrent neural networks, the states, connection weights, as well as activation functions are all defined in complex domain, thus, it is an extension of real-valued system. In this paper, by means of an appropriate Lyapunov functional, contraction mapping theory and nonlinear measure method, some sufficient conditions are presented to ascertain the existence, uniqueness and stability of the equilibrium point for the given fractional order complex-valued systems. The obtained results can be easily applied to the complex-valued neural networks whether their activation functions are expressed by separating their real and imaginary parts or not. Finally, simulation examples are presented to show the usefulness of our theoretical results.

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Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term

Cited by 101 publications

References 33 publications

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

Delay-dependent stability criteria for neutral-type neural networks with interval time-varying delay signals under the effects of leakage delay

Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays

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