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 xi,t+1=f(xi,t)+Cᵢ(xi,t,x_i-1,t)+D(xi,t,x_i-1,t), where f:R→R is a nonlinear map, and Cᵢ,{D}ᵢ:$ ${R}²{→}R$ 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.