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Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise

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  • The longtime and global pullback dynamics of stochastic Hind-marsh-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 $ L^2 $ Hilbert space.

    Mathematics Subject Classification: Primary: 35K55, 35Q80, 37L30, 37L55, 37N25; Secondary: 35B40, 60H15, 92B20.

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  • Figure 1.  Time responses of the membrane potential for various value of the stimulated current: (a) resting state when J = 0, (b) tonic spiking when J = 1.2, (c) regular bursting when J = 2.2, (d) chaotic bursting when J = 3.1, (e) the x-z phase portrait when J = 2.2, (f) the x-z phase portrait when J = 3.1. Source: [25]

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