EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS
Copyright policy )EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS
The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the squeezing property of an abstract reaction-diffusion equation also proved in this paper. The results infer that the global attractor whose existence has been established in [23] for the Hindmarsh-Rose semiflow has a finite fractal dimension.
arXiv admin note: text overlap with arXiv:1907.13225
diffusive Hindmarsh-Rose equations, PDEs in connection with biology, chemistry and other natural sciences, exponential attractor, squeezing property, Dynamical systems in biology, Mathematics - Analysis of PDEs, Reaction-diffusion equations, Neural biology, FOS: Mathematics, compact absorbing set, Attractors, finite fractal dimension, Initial-boundary value problems for second-order parabolic systems, Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems, Analysis of PDEs (math.AP)
diffusive Hindmarsh-Rose equations, PDEs in connection with biology, chemistry and other natural sciences, exponential attractor, squeezing property, Dynamical systems in biology, Mathematics - Analysis of PDEs, Reaction-diffusion equations, Neural biology, FOS: Mathematics, compact absorbing set, Attractors, finite fractal dimension, Initial-boundary value problems for second-order parabolic systems, Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems, Analysis of PDEs (math.AP)
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