COMPUTING LYAPUNOV EXPONENTS IN COUPLED MAP LATTICE FOR CONTROLLING SPATIOTEMPORAL CHAOS

The most common and useful tool for the characterization of chaos is given by the Lyapunov exponents. In this paper, the computation of the entire Lyapunov exponents of the coupled logistic map lattice is considered. For this, the Jacobian matrix of coupled map lattice with constant coupling strength is first determined. The conditions of multiplicative ergodic theorem for nonlinear coupled map lattice are proven and then the Jacobian matrix of this map in order to computing Lyapunov exponents is calculated. The feasibility of this approach is illustrated in one system. The method for controlling spatiotemporal chaos based on Lyapunov exponents is also explained.