Mutual synchronization of switchings in coupled chaotic systems
V.S. Anishchenko, A.N. Silchenko, I.A. Khovanov
Laboratory of Nonlinear Dynamics, Saratov State University
As known there are two classical bifurcational mechanisms of
synchronization:
1) locking of the frequency oscillations which takes place both in the
nonautonomous case and in the case of symmetrically coupled self-sustained
oscillators,
2)suppression of natural oscillations by the external signal (or suppression
of oscillations of one of the coupled subsystems by the signal of the other
subsystem).
In [1] it was proposed to generalize the classical conception of synchronization for a certain class of chaotic systems whose basic frequencies can be distinguished in the power spectrum.
It was shown [2,3] that the phenomenon like frequency locking may be observed in stochastic bistable systems. In [2] the stochastic bistable system driven by external periodic force was considered. It was shown that the effect of mean switching frequency locking takes place. The region on the parameter plane "noise intensity - amplitude of periodic excitation" which corresponds to this phenomenon is similar to the synchronization (phase locking) region in the classical theory of oscillations.
In [3] two symmetrically coupled bistable stochastic systems were investigated. It has been established that the stochastic processes in subsystems become coherent at some critical value of coupling and the effect of the Kramers rates locking takes place. This effect was called stochastic synchronization.
Taking into account the mentioned above, it is reasonable to consider the case when the transitions between two states in symmetrically coupled bistable systems are caused by the natural dynamics of subsystems instead of source of noise. To realise this case it is necessary to use a deterministic chaotic system which possesses dynamical intermittency of "chaos - chaos" type [4]. "Random switchings" between two chaotic attractors in this regime take place in the absence of noise. By analogy with the case of coupled stochastic bistable systems the processes of switchings in subsystems can be characterized by the mean switching frequency.
In this work we investigated two symmetrically coupled chaotic systems with dynamical intermittency of "chaos - chaos" type (two coupled Chua's circuits and two coupled Lorenz systems were considered). We have found that the mean switching frequencies in the subsystems draw closer to one another when the coupling is increased and they coincide at some critical value of the coupling.
Thus, we may speak about the effect of mutual synchronization of the "random" processes of switchings in two coupled systems, each of them is characterized by the chaotic bistable dynamic in the absence of noise.