Multistability of Almost Periodic Solution for Memristive Cohen-Grossberg Neural Networks With Mixed Delays

Qin, Sitian; Ma, Qiang; Feng, Jiqiang; Xu, Chen

doi:10.1109/tnnls.2019.2927506

Cited by 30 publications

(12 citation statements)

References 34 publications

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“…Cohen-Grossberg neural network which takes some famous neural networks and systems such as Hopfield neural networks and Lotka-Volterra system as its special cases, was first proposed by Cohen and Grossberg [43,44]. In the past few years, memristive Cohen-Grossberg neural network (MCGNNs) and its dynamical characteristics have been widely investigated [45][46][47][48][49][50]. In [45,46], the exponential synchronization issue of MCGNNs with delays was discussed.…”

Section: Introductionmentioning

confidence: 99%

“…Using the fixed point theorem, Nie et al addressed the multistability topic of MCGNNs and obtained 3 n exponentially stable equilibrium points for n-dimensional MCGNNs with piecewise linear activation functions [47]. Multistability of MCGNNs with mixed delays was discussed and multiple almost periodic solutions were obtained in [49]. In [50], global exponential stability of MCGNNs with mixed delays and impulse perturbations was investigated.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Introductionmentioning

confidence: 99%

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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“…Recently, the multistability research of CGNN has achieved some results [6][7][8][9][10][11][12]. Nie et al [7] investigated equilibrium points of the MCGNN by using the fixed point and nonsmooth analysis theory.…”

Section: Introductionmentioning

confidence: 99%

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

Li,

Zhao,

Zhang

et al. 2023

Math Methods in App Sciences

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Based on the relevant theories of M‐matrix and the Lyapunov stability technique, this paper investigates the multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks. With the help of Cauchy convergence criterion, the exponential stability inequality is derived. The system has locally exponentially stable equilibrium points and periodic solutions, which greatly increases the number of solutions compared with the existing Cohen–Grossberg neural networks, where the is a Clifford‐valued and there is no limitation of linearity and monotonicity for activation functions. Furthermore, the attraction basins of stable periodic solutions are obtained, and it is proved that the basins can be enlarged. It is worth mentioning that the results can also be used to discuss the multistability of equilibrium points, periodic solutions, and almost periodic solutions for real‐valued, complex‐valued, and quaternion‐valued memristive Cohen–Grossberg neural networks. Finally, two numerical examples with simulations are taken to verify the theoretical analysis.

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“…The Cohen-Grossberg neural network is a generalized neural network model, which can take famous neural networks and systems such as the Hopfield neural network and Lotka–Volterra system as its special cases [ 17 , 18 , 19 ]. In recent years, memristive Cohen-Grossberg neural network (MCGNN) and its dynamical characteristics have attracted increasing attention [ 20 , 21 , 22 , 23 ]. In [ 21 ], there exist exponentially stable equilibrium points in n-dimensional MCGNNs with piecewise linear activation functions via the fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

“…Global exponential stability of delayed and perturbed MCGNNs was investigated in [ 22 ]. Paper [ 23 ] studied multistability of MCGNNs with mixed delays and acquired multiple almost periodic solutions. Synchronization as one of the most important dynamical characteristics has been researched extensively and many papers on synchronization of MCGNNs have been published [ 24 , 25 , 26 , 27 , 28 ].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

Yao

Zhang

et al. 2022

Micromachines

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This paper investigates the asymptotic synchronization of memristive Cohen–Grossberg neural networks (MCGNNs) with time-varying delays under event-triggered control (ETC). First, based on the designed feedback controller, some ETC conditions are provided. It is demonstrated that ETC can significantly reduce the update times of the controller and decrease the computing cost. Next, some sufficient conditions are derived to ensure the asymptotic synchronization of MCGNNs with time-varying delays under the ETC method. Finally, a numerical example is provided to verify the correctness and effectiveness of the obtained results.

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Multistability of Almost Periodic Solution for Memristive Cohen-Grossberg Neural Networks With Mixed Delays

Cited by 30 publications

References 34 publications

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

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

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

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