Yiqian Wang

Chaotic Synchronization in Coupled Map Lattices with Periodic Boundary Conditions

In this paper, we consider a lattice of the coupled logistic map with periodic boundary conditions. We prove that synchronization occurs in the one-dimensional lattice with lattice size n = 4 for any γ in the chaotic regime (γ∞ ≈ 3.57, 4). It is worthwhile to emphasize that, despite of the fact that there is a rigorous proof for synchronization in many systems with continuous time, almost nothing is rigorously proved for the systems with discrete time.

INVARIANT TORI IN NONLINEAR OSCILLATIONS

The boundedness of all the solutions for semilinear Duffing equationx″ + ω2x + φ(x) =p(t), ω ∈ ℝ+ℕ is proved, wherep (t) is a smooth 2π-periodic function and the perturbation ⌽(x) is bounded.

Existence of quasiperiodic solutions and Littlewood's boundedness problem of super-linear impact oscillators

Abstract So far most application of Kolmogorov–Arnold–Moser (KAM) theory has been restricted to smooth dynamical systems. In this paper, it is shown by a series of transformations that how KAM theory can be used to analyze the dynamical behavior of Duffing-type equations with impact. The analysis is carried out for the example (0.1) x ¨ + x 2 n + 1 = p ( t ) , for x ( t ) > 0 , x ( t ) ⩾ 0 , x ˙ ( t 0 + ) = - x ˙ ( t 0 - ) , if x ( t 0 ) = 0 with p xa0∈xa0 C 5 being periodic. We prove that all solutions are bounded, and that there are infinitely many periodic and quasiperiodic solutions in this case.

PROOF OF SYNCHRONIZED CHAOTIC BEHAVIORS IN COUPLED MAP LATTICES

In this paper, we consider chaotic synchronization in coupled map lattices (CMLs) with periodic boundary conditions. We give a rigorous proof of the occurrence of synchronization for 1D such CMLs with lattice size n = 5 for suitable parameters in the chaotic regime by Lyapunov method.

SYNCHRONIZATION AND ASYNCHRONIZATION IN A LATTICE OF COUPLED LORENZ-TYPE MAPS

In this paper, we study synchronization and asynchronization in a Coupled Lorenz-type Map Lattice (CLML). Lorenz-type map forms a chaotic system with an appropriate discontinuous function. We prove that in a CLML with suitable coupling strength, there is a subset of full measure in the phase space such that chaotic synchronization occurs for any orbit starting from this subset and there is a dense subset of measure zero in the phase space such that synchronization will never occur. We also provide numerical observations to explain our results.