Controlling hyperchaos and periodic state synchronization of degenerate optical parametric oscillators

Hyperchaotic control and periodic synchronization between two degenerate optical parametric oscillators are presented by mutual coupling parameter modulation, based on the nonlinear kinetic characteristic of degenerate optical parametric oscillator. Theoretical results show that the two degenerate optical parametric oscillators in hyperchaotic state can be controlled into periodic output by mutual couple, no matter whether the two degenerate optical parametric oscillators are identical. It is also shown that the periodic states can result in identical synchronization or anti-synchronization only in the case where the largest Lyapunov exponent of the system is negative. Thus synchronization type and evolution process of synchronization are determined by modulating coefficient and initial conditions.