Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative Noise

Phan, Chi

doi:10.48550/arxiv.1908.01220

Cited by 4 publications

(4 citation statements)

References 34 publications

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“…Recently it has been proved by the two authors of this paper and J. Su in [24] that there exist global attractors for the diffusive and partly diffusive Hindmarsh-Rose equations. We have also shown in [23] that there exists a random attractor for the stochastic Hindmarsh-Rose equations with multiplicative noise.…”

Section: Introductionmentioning

confidence: 77%

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Random Attractor for Stochastic Hindmarsh–Rose Equations with Additive Noise

Phan

You

2019

J Dyn Diff Equat

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For stochastic Hindmarsh-Rose equations with additive noises in the study of neurodynamics, the longtime and global pullback dynamics on a twodimensional bounded domain is explored in this work. Using the additive transformation and by the sharp uniform estimates, we proved the pullback absorbing and the pullback asymptotically compact characteristics of the Hindmarsh-Rose random dynamical system in the L 2 Hilbert space. It shows the existence of a random attractor for this random dynamical system.2000 Mathematics Subject Classification. Primary: 35K55, 35Q80, 37L30, 37L55, 37N25 ; Secondary: 35B40, 60H15, 92B20.

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Section: Introductionmentioning

confidence: 77%

“…Very recently, we have proved the existence of a random attractor for the stochastic Hindmarsh-Rose equations with multiplicative noise in [23].…”

Section: Introductionmentioning

confidence: 99%

Random Attractor for Stochastic Hindmarsh–Rose Equations with Additive Noise

Phan

You

2019

J Dyn Diff Equat

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“…In recent work [13,14,15,16], the authors studied the single neuron model of diffusive Hindmarsh-Rose equations and proved the existence of global attractor and pullback random attractor for the solution semiflow and the solution cocycle.…”

Section: Synchronization Of Biological Neurons Is One Of the Central ...mentioning

confidence: 99%

Synchronization of Boundary Coupled Hindmarsh-Rose Neuron Network

Phan¹,

You²

2019

Preprint

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In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh-Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed a quantified threshold in terms of the parameters.

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“…Very recently, the authors in [30] and [29] proved the existence of global attractors for the diffusive and partly diffusive Hindmarsh-Rose equations as well as the existence of a random attractor for the stochastic Hindmarsh-Rose equations with multiplicative noise.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of nonautonomous Hindmarsh–Rose equations

Phan

You

2020

Nonlinear Analysis: Real World Applications

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Global dynamics of nonautonomous diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback dissipative property and the pullback asymptotical compactness. Then the existence of pullback exponential attractor is also established by proving the smoothing Lipschitz continuity in a long run of the solution process.

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Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative Noise

Cited by 4 publications

References 34 publications

Random Attractor for Stochastic Hindmarsh–Rose Equations with Additive Noise

Random Attractor for Stochastic Hindmarsh–Rose Equations with Additive Noise

Synchronization of Boundary Coupled Hindmarsh-Rose Neuron Network

Global dynamics of nonautonomous Hindmarsh–Rose equations

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