Controlling hyperchaos and periodic synchronization in DOPO with parameter modulated by an external periodic signal

Hyperchaotic behaviors can be controlled and converted into periodic behaviors by modulating the detuned parameters using an external periodic signal in degenerated optical parameter oscillator (DOPO). Numerical simulations show that the period number differs on the account of the modulating coefficient. Increasing the modulating coefficient, the DOPO results in conversion to periodic orbits. Subsequently it is converted into period 2, and then into period 1. It was also shown that the periodic orbits of the DOPOs modulated through external periodic signal can result in identical synchronization or anti-synchronization only in the case that the largest Lyapunov exponent of the system is negative. Thus synchronization types and evolution process of synchronization is determined by modulating coefficient and initial conditions.