Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative Noise

2019/08/03 by Chi Phan, Phan, Chi · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations #math.AP #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1908.01220

openalex publication_date 2019/08/03 · arxiv created 2019/08/13 · arxiv updated 2019/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this random dynamical system is proved through the exponential transformation and uniform estimates showing the pullback absorbing property and the pullback asymptotically compactness of this cocycle in the L² Hilbert space.

Citations

• Random dynamical systems
• A quantitative description of membrane current and its application to conduction and excitation in nerve
• Impulses and Physiological States in Theoretical Models of Nerve Membrane
• Global Attractors for Hindmarsh-Rose Equations in Neurodynamics

Cited by

• Random Attractor for Stochastic Hindmarsh-Rose Equations with Additive Noise
• Global Dynamics of Nonautonomous Hindmarsh-Rose Equations

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