Stability analysis of fraction-order Hopfield neuron network and noise-induced coherence resonance
type: Item
instance of: scholarly article
title: Stability analysis of fraction-order Hopfield neuron network and noise-induced coherence resonance
zbMATH Open document ID: 1459.92021
DOI: 10.1155/2020/3520972
published in: Mathematical Problems in Engineering
publication date: 2020-07-23T00:00:00Z
review text: Summary: In this paper, dynamical behaviors of fraction-order Hopfield neuron network are investigated. Firstly, Mittag-Leffler stability analysis is carried out and some sufficient conditions are obtained. On the basis of theoretical analysis, two criteria for determining the stability of fraction-order Hopfield neuron network are presented and comparison between them is given by theoretical analysis along with numerical simulation. According to the proposed criteria, by selecting suitable system parameters, it can be obtained that fraction-order Hopfield neuron network can stabilize to the equilibrium point or an attractor, which can be a periodic orbit or two points. Secondly, considering the inevitable noise in the complex environment of neuron network, the effect of noise on the dynamics of fraction-order Hopfield neuron network is discussed via calculating coefficient of variation and numerical simulations. Results suggest that random noise can cause coherence resonance in fraction-order Hopfield neuron network for certain noise intensity.
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34F15
zbMATH DE Number: 7224356
author: Xuerong Shi
author: Zuolei Wang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/3520972
OpenAlex ID: W3037998745
cites work: Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors
cites work: Synchronization realization between two nonlinear circuits via an induction coil coupling
cites work: Synchronization control between two Chua's circuits via capacitive coupling
cites work: Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse
cites work: Globally exponentially robust stability and periodicity of delayed neural networks
cites work: Effects of coupling strength and network topology on signal detection in small-world neuronal networks
cites work: Neurons with graded response have collective computational properties like those of two-state neurons.
cites work: Coexistence of multiple stable states and bursting oscillations in a 4D Hopfield neural network
cites work: A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
cites work: Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
cites work: \(PD^\vartheta\) control strategy for a fractional-order chaotic financial model
cites work: Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks
cites work: Influence of multiple time delays on bifurcation of fractional-order neural networks
cites work: Bifurcation analysis for a fractional‐order chemotherapy model with two different delays
cites work: Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons
cites work: Control scheme for a fractional-order chaotic Genesio-Tesi model
cites work: Stability and bifurcation of a delayed generalized fractional-order prey-predator model with interspecific competition
cites work: Bifurcation of a fractional-order delayed malware propagation model in social networks
cites work: On Hopf bifurcation in fractional dynamical systems
cites work: \(\alpha\)-stability and \(\alpha\)-synchronization for fractional-order neural networks
cites work: Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays
cites work: Multiple Mittag-Leffler stability of fractional-order competitive neural networks with Gaussian activation functions
cites work: Q4250595
cites work: Q5699297
cites work: Mittag-Leffler stability of fractional order nonlinear dynamic systems
cites work: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
cites work: Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks
cites work: A predictor-corrector approach for the numerical solution of fractional differential equations
cites work: Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons
description: scientific article; zbMATH DE number 7224356