ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

2001/01/01 by Peter W. Bates, PETER W. BATES, KENING LU +3 · 6 citations
Engineering · Computer Science · #Stability and Controllability of Differential Equations #Nonlinear Dynamics and Pattern Formation #Advanced Mathematical Modeling in Engineering

paper · doi:10.1142/s0218127401002031

Abstract

We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.

Citations

• Traveling Waves in Lattice Dynamical Systems
• A Discrete Convolution Model¶for Phase Transitions

Cited by

• Almost Periodic Solutions of Lattice Dynamical Systems with Monotone Nonlinearity
• ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS
• RANDOM ATTRACTORS FOR SECOND ORDER STOCHASTIC LATTICE DYNAMICAL SYSTEMS WITH MULTIPLICATIVE NOISE IN WEIGHTED SPACES
• Random attractors for second-order stochastic lattice dynamical systems
• Upper-semicontinuity of attractors for random lattice systems perturbed by small white noises
• Global existence in infinite lattices of nonlinear oscillators: The Discrete Klein-Gordon equation

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• Global Attractors of Non-autonomous Lattice Dynamical Systems
• Lattice Structures for Attractors II
• Lattice Structures for Attractors I
• Lattice Structures for Attractors III
• On the forward dynamical behavior of nonautonomous lattice dynamical systems