Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks

This work is chiefly concerned with the stability behavior and the appearance of Hopf bifurcation of fractional-order delayed Cohen–Grossberg neural networks. Firstly, we study the stability and the appearance of Hopf bifurcation of the involved neural networks with identical delay ϑ 1 = ϑ 2 = ϑ . Secondly, the sufficient criterion to guarantee the stability and the emergence of Hopf bifurcation for given neural networks with the delay ϑ 2 = 0 is set up. Thirdly, we derive the sufficient condition ensuring the stability and the appearance of Hopf bifurcation for given neural networks with the delay ϑ 1 = 0 . The investigation manifests that the delay plays a momentous role in stabilizing networks and controlling the Hopf bifurcation of the addressed fractional-order delayed neural networks. At last, software simulation results successfully verified the rationality of the analytical results. The theoretical findings of this work can be applied to design, control, and optimize neural networks.

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Stochastic exponential synchronization for delayed neural networks with semi-Markovian switchings: Saturated heterogeneous sampling communication

Nonlinear Analysis Hybrid Systems ◽

10.1016/j.nahs.2021.101028 ◽

2021 ◽

Vol 41 ◽

pp. 101028

Author(s):

Xiaoqing Li ◽

Sing Kiong Nguang ◽

Kun She ◽

Jun Cheng ◽

Kaibo Shi ◽

...

Keyword(s):

Neural Networks ◽

Exponential Synchronization ◽

Delayed Neural Networks

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Robust synchronization of uncertain delayed neural networks with packet dropout using sampled-data control

Applied Intelligence ◽

10.1007/s10489-021-02388-1 ◽

2021 ◽

Author(s):

Ganlei Zhang ◽

Jiayong Zhang ◽

Wei Li ◽

Chao Ge ◽

Yajuan Liu

Keyword(s):

Neural Networks ◽

Packet Dropout ◽

Sampled Data ◽

Delayed Neural Networks ◽

Robust Synchronization ◽

Data Control ◽

Sampled Data Control

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Adaptive state estimation of Markov switched neural networks driven by Lévy noise

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219869472 ◽

2019 ◽

Vol 42 (2) ◽

pp. 330-336

Author(s):

Dongbing Tong ◽

Qiaoyu Chen ◽

Wuneng Zhou ◽

Yuhua Xu

Keyword(s):

Neural Networks ◽

State Estimation ◽

Sufficient Conditions ◽

Lyapunov Stability Theory ◽

Lévy Noise ◽

Linear Matrix ◽

Delayed Neural Networks ◽

Switched Neural Networks ◽

Inequality Technique ◽

Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

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