Dynamics of systems on infinite lattices

By Bixiang Wang. 2006

172 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/54cda4e868a40d6eedd8dd2c605d93c93d73af66

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In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Invariant measures of stochastic delay lattice systems (2021, background): “The solutions and their long-term dynamics of deterministic lattice systems have been studied in [1, 2, 3, 17, 24, 25, 26, 34, 67] and [4, 8, 16, 18, 19, 39, 52, 60], respectively.”
Global existence and compact attractors for the discrete nonlinear Schrödinger equation (2005, result): “We also refer to the very recent work [40].”
Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise (2015, background): “The attractors of lattice equations have been investigated in [3,7,24,33,44] in the deterministic case, in [5,8,12,23,37,45] in the autonomous stochastic case, and in [6] in the non-autonomous stochastic case.”
Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, methodology): “, ε = 0), traveling waves of lattice systems have been investigated in [1, 4, 5, 20, 30, 31, 32, 62], the chaotic properties of solutions have been studied in [19, 21, 22], and global attractors have been explored in [6, 10, 43, 49, 60].”
Asymptotic behavior of non-autonomous lattice systems (2007, background): “Such compactness in [6,26] was obtained by the uniform estimates on the tails of solutions with a bounded set of initial data when t → ∞.”
Pullback Exponential Attractors for Non-autonomous Lattice Systems (2012, unknown): “(2) Following the idea of [14,39], we next extend our result from l2 to l2 ρ to show that for any uτ ∈ l2 ρ and g ∈ G , (8) has a mild solution u(t, τ ; uτ , g) on [τ, τ + T ) with u(τ, τ ; uτ , g) = uτ .”