Periodic States in Chaotic R?ssler Oscillators with On-Off Coupling

It has been revealed that two coupled chaotic R?ssler oscillators can transit to a period-5 splay state in an extremely weak coupling region Zhan et al., Phys. Rev. Lett. 86 (2001) 1510. Here we show that with further increase of coupling, two other coupling regions exist that may induce the period-4 splay state and period-5 synchronous state. Using an on-off coupling strategy, we find that the coupling regions for inducing period-5 states can be significantly extended and the extending effect is regulated by the match of two time scales: one is of the on-off coupling and the other is of the individual R?ssler oscillator. We then compare the sensitivity of the periodic states with the initial conditions of the oscillators. We also analyze the mechanism behind these two new types of periodic states.