On the Stabilization of Internally Coupled Map Lattice Systems

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.