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 x i , t + 1 = G ( ( 1 − α i − β i ) x i , t + α i x i + 1 , t + β i x i − 1 , t ) , where f : ℝ → ℝ is a nonlinear map, and α and β are nonnegative coupling constants that satisfy the constraint α i + β i < 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.