Long term behavior of a random Hopfield neural lattice model

DOI10.3934/cpaa.2019039zbMath1404.37093OpenAlexW2898273498WikidataQ129035710 ScholiaQ129035710MaRDI QIDQ1633414

Basiru Usman, Xiaoying Han, Peter E. Kloeden

Publication date: 20 December 2018

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2019039

zbMATH Keywords

random attractorHopfield neural networkrandom dynamical systemneural lattice modelrandom ordinary differential equation

Mathematics Subject Classification ID

Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Neural networks for/in biological studies, artificial life and related topics (92B20) Generation, random and stochastic difference and differential equations (37H10) Infinite-dimensional random dynamical systems; stochastic equations (37L55) Ordinary lattice differential equations (34A33)

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Periodic measures of impulsive stochastic neural networks lattice systems with delays, Random attractors for stochastic discrete complex Ginzburg–Landau equations with long-range interactions, Periodic measures of reaction-diffusion lattice systems driven by superlinear noise, Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise, Periodic measures of impulsive stochastic Hopfield-type lattice systems, Pullback and forward dynamics of nonautonomous Laplacian lattice systems on weighted spaces, Non-autonomous stochastic lattice systems with Markovian switching, Upper semi-continuous convergence of attractors for a Hopfield-type lattice model, Convergence and Approximation of Invariant Measures for Neural Field Lattice Models under Noise Perturbation, Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains, Stochastic dynamics of a neural field lattice model with state dependent nonlinear noise, Wong-Zakai approximations of stochastic lattice systems driven by long-range interactions and multiplicative white noises, Stability analysis of Hopfield neural networks with unbounded delay driven by G-Brownian motion

Cites Work

• Unnamed Item
• Unnamed Item
• A study of the application of Kohonen-type neural networks to the travelling salesman problem
• Dynamics of systems on infinite lattices
• Asymptotic behavior of non-autonomous lattice systems
• Global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity
• Attractors for random dynamical systems
• Monotone random systems theory and applications
• Attractors for second order lattice dynamical systems
• Pullback attractors for asymptotically compact non-autonomous dynamical systems
• Attractors for lattice fitzHugh--Nagumo systems
• Random attractors for the 3d stochastic navier-stokes equation with multiplicative white noise
• Lifted Lattices, Hyperbolic Structures, and Topological Disorders in Coupled Map Lattices
• Random Ordinary Differential Equations and Their Numerical Solution
• Neurons with graded response have collective computational properties like those of two-state neurons.
• ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS
• ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS
• Stochastic Equations in Infinite Dimensions