On the stabilization of internally coupled map lattice systems

Abstract

The adaptive adjustment mechanism is applied to the stabilization of an internally coupled map lattice system defined by xi,t+1=G((1−αi−βi)xi,t+αixi+1,t+βixi−1,t), where f:ℝ→ℝ is a nonlinear map, and α and β are nonnegative coupling constants that satisfy the constraint αi+βi<1, for all x∈ℝ, i=1,2,…,n. Sufficient conditions and ranges of adjustment parameters that guarantee the local stability of a generic steady state have been provided. Numerical simulations have demonstrated the effectiveness and efficiency for this mechanism to stabilize the system to a generic unstable steady state or a periodic orbit.