Exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays

Zhou, Liqun; Zhao, Zhixue

doi:10.1016/j.neucom.2019.09.046

Cited by 32 publications

(8 citation statements)

References 32 publications

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“…In 1996, Yang and Yang 1 proposed the fuzzy cellular neural networks. Based on Reference 1, in recent several years, some important synchronization control of delayed fuzzy neural networks have been proposed, such as asymptotical synchronization, [2][3][4] exponential synchronization, [5][6][7][8][9] , 10 and so on. Meanwhile, there are synchronization control of delayed neutral-type neural networks due to the complicated dynamic properties of the neural cells in the real-world and neutral neural networks contain some information about the derivative of the past state.…”

Section: Previous Workmentioning

confidence: 99%

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

Kong

Sakthivel

2020

Intl J Robust & Nonlinear

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This paper aims to investigate the general decay synchronization analysis of discontinuous fuzzy neutral-type neural networks. Under the framework of Filippov solutions, based on functional differential inclusions theory, inequality technique and by constructing a modified delay-dependent Lyapunov-Krasovskii functional, some new delay-dependent criteria are provided to guarantee the general decay synchronization via the effective nonlinear feedback controller. The neural network model considered is more generalized, some previous fuzzy neural networks can be regard as the special cases. Moreover, some recent results on the delay-independent criteria ensuring the general decay synchronization can also be extended and concluded. These can be seen from the given corollaries and remarks which are provided to make the comparisons and show the advantages. Finally, some numerical examples and simulations are provided to illustrate the correctness.

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Section: Previous Workmentioning

confidence: 99%

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

Kong

Sakthivel

2020

Intl J Robust & Nonlinear

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“…Dhama1 and Abbas [7] made a systematic analysis on the existence and stability of weighted pseudo almost automorphic solution of dynamic equation. Zhou and Zhao [32] studied the synchronization issue of a class of neural networks with proportional delays. For more detailed contents on these aspects, we refer the readers to [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Liu

et al. 2022

NAMC

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In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.

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“…Using the appropriate Lyapunov–Krasovski functionals and applying matrix inequality approach methods, Zhou [ 21 ] discussed the passivity of a class of recurrent neural networks with impulse and multiproportional delays. Zhou and Zhao [ 22 ] investigated the exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays. Robust stability analysis of recurrent neural networks is studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays

Meng

et al. 2022

Computational Intelligence and Neuroscience

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This paper investigates the bifurcation issue of fractional-order four-neuron recurrent neural network with multiple delays. First, the stability and Hopf bifurcation of the system are studied by analyzing the associated characteristic equations. It is shown that the dynamics of delayed fractional-order neural networks not only depend heavily on the communication delay but also significantly affects the applications with different delays. Second, we numerically demonstrate the effect of the order on the Hopf bifurcation. Two numerical examples illustrate the validity of the theoretical results at the end.

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Exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays

Cited by 32 publications

References 32 publications

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays

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