Multistability of discrete-time delayed Cohen–Grossberg neural networks with second-order synaptic connectivity

Yang, Wu; Wang, Yan‐Wu; Zeng, Zhigang; Zheng, Ding-Fu

doi:10.1016/j.neucom.2015.02.064

Cited by 22 publications

(14 citation statements)

References 38 publications

(59 reference statements)

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“…In literatures [15,16,17,18,19,20], [26,27,28,29,30,31], [45,46], synchronization was addressed under a stable equilibrium state. As discussed previously, multiple stable equilibrium states are very necessary for coupled systems including CMMNNs in some applications [12,13,14], [23,24], [32,33,34], [36,37,38,39,40,41,42]. Therefore, when coupled systems have multiple stable equilibrium states, how to achieve synchro- [32].…”

Section: Introductionmentioning

confidence: 99%

“…As one of the most important dynamic characteristics, multistability of complex dynamical systems has been extensively investigated in recent years [12,13,14], [37,38,39,40,41]. For example, papers [37,38,39,40,41] researched multistability of NNs. Wu and Zhang analyzed multistability of delayed MNNs with PLAF having 2 corner points in [13].…”

Section: Introductionmentioning

confidence: 99%

“…In the above researches [13,14], MNNs can only obtain a small quantity of stable e-quilibrium states with a few corner points. Actually, as many stable equilibrium states as possible are very necessary for coupled systems including CMMNNs in some applications [12,13,14], [23,24], [32,33,34], [36,37,38,39,40,41,42], such as associative memory storage, image processing.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

et al. 2019

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In this paper, we focus on synchronization issue of coupled multistable memristive neural networks (CMMNNs) with time delay under multiple stable equilibrium states. First, we build delayed CMMNNs consisting of one master subnetwork without controller and N − 1 identical slave subnetworks with controllers, and every subnetwork has n nodes. Moreover, this paper investigates multistability of delayed CMMNNs with continuous nonmonotonic piecewise linear activation function (PLAF) owning 2r + 2 corner points. By using the theorems of differential inclusion and fixed point, sufficient conditions are derived such that master subnetwork of CMMNNs can acquire (r + 2) n exponentially stable equilibrium points, stable periodic orbits or hybrid stable equilibrium states. Then, this paper proposes hybrid multisynchronization of delayed CMMNNs related with various external inputs under multiple stable equilibrium states for the first time. There exist (r + 2) n hybrid multisynchronization manifolds in CMMNNs with different initial conditions and external inputs. Finally, two numerical simulations are given to illustrate the effectiveness of the obtained results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

et al. 2019

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“…Multistability, an important dynamical characteristic of neural networks, has been extensively investigated in recent years [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. For example, Kaslik and Sivasundaram researched multistability of discrete-time Hopfield NNs with distributed delays and impulses [25].…”

Section: Introductionmentioning

confidence: 99%

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

Yao

Wang

Sun

et al. 2020

Applied Mathematics and Computation

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Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or evensequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w + 2) l (or (w + 1) l ) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.

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“…Thus it is necessary that there exist multiple stable equilibrium points for neural networks. The coexistence of multiple equilibrium points and their local stability, which is usually referred to as the multistability of neural network models, has been reported in depth in the last years (see [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] and the references therein). Wang et al in [35] studied a class of neural networks with r-level piecewise linear nondecreasing activation functions and showed that the n-neuron dynamical system had exact (2r + 1) n equilibrium points, of which (r + 1) n were locally exponentially stable and the others were unstable.…”

Section: Introductionmentioning

confidence: 99%

Multiple stability and instability of Cohen–Grossberg neural network with unbounded time-varying delays

Chen

Jia

2019

J Inequal Appl

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In this paper, multiple stability and instability of Cohen-Grossberg neural network with unbounded time-varying delays are studied. Based on the geometrical configuration of activation functions and some rigorous mathematical analysis, some algebraic criteria are proposed to guarantee coexistence of multiple stable equilibrium points and multiple unstable equilibrium points in the model. Moreover, using the partition space method, we prove that the discussed model has at least 3 n equilibrium points, 2 n of them are locally μ-stable and others are unstable. Finally, the numerical example and its simulation show the effectiveness of the proposed results.

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Multistability of discrete-time delayed Cohen–Grossberg neural networks with second-order synaptic connectivity

Cited by 22 publications

References 38 publications

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

Multiple stability and instability of Cohen–Grossberg neural network with unbounded time-varying delays

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