Matrix measure based stability criteria for high-order neural networks with proportional delay

Zheng, Cong; Li, Ning; Cao, Jinde

doi:10.1016/j.neucom.2014.09.016

Cited by 53 publications

(21 citation statements)

References 35 publications

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“…That is, the claim (31) must hold. We use (28) in (31) to obtain (14) which asserts the global exponential stability of (u * , v * ) T of (7). The proof is completed.…”

Section: Consider the Following Functions U(t) And V (T) Defined Bymentioning

confidence: 99%

“…In an amount of parallel pathways, affected by different materials and topology, there may be some unbounded delays which is proportional to the time, so we should choose proper proportional delays factors according to different cases and adopt proportional delays to characterize these unbounded delays. At present, results of dynamical behaviors for neural networks with proportional delays have a few [20,[23][24][25][26][27][28]. In [23], dissipativity of a class of cellular neural networks (CNNs) with proportional delays was investigated by using the inner product properties.…”

Section: Introductionmentioning

confidence: 99%

“…Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays was studied in [27] by constructing appropriate Lyapunov functional, several new delay-dependent and decentralized control laws, which are related to the size of the proportional delay factors, were derived to achieve the exponential synchronization. In [28], stability criteria for high-order networks with proportional delay was studied based on matrix measure, Lyapunov functional and Halanay inequality.…”

Section: Introductionmentioning

confidence: 99%

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Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

Zhou

2015

Neurocomputing

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“…That is, the claim (31) must hold. We use (28) in (31) to obtain (14) which asserts the global exponential stability of (u * , v * ) T of (7). The proof is completed.…”

Section: Consider the Following Functions U(t) And V (T) Defined Bymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

Zhou

2015

Neurocomputing

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“…In [22], the exponential stability of high-order neural networks with proportional delay is investigated by using the Lyapunov method and matrix measure. Based on the nonsmooth…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Synchronization for a Class of Fractional-Order Neural Networks

Liu

2016

Entropy

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Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall-Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods.

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“…Zheng et al . established the stability criteria for high‐order networks with proportional delay. We must point out that BAM neural networks with proportional delays have been widely applied in many fields such as light absorption in the star substance and nonlinear dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

Pang

2016

Math Methods in App Sciences

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This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.

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Matrix measure based stability criteria for high-order neural networks with proportional delay

Cited by 53 publications

References 35 publications

Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

Stability Analysis and Synchronization for a Class of Fractional-Order Neural Networks

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

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