Stabilizing coupled map lattice systems with adaptive adjustment

The adaptive adjustment mechanism is applied to stabilization of a general coupled-map lattice system defined by x_i,t+1=f(x_i,t)+C_i(x_i,t,x_i-1,t)+D(x_i,t,x_i-1,t), where f: R→R is a nonlinear map, and C_i,D_i: R²→R are coupling functions that satisfy C_i(x,x)=0 and D_i(x,x)=0, ∀ x∈R, i=1,2,…,n. Sufficient conditions and ranges of adjustment parameters that guarantee the local stability of a synchronized fixed point are provided. Numerical simulations demonstrate the effectiveness and efficiency for this mechanism to stabilize the system to an originally unstable synchronized fixed point or a periodic orbit.