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.