The peculiarities of the effect of the
locking MSF by external force in system
with dynamical intermittency
I.A. Khovanov, V.S. Anishchenko
Laboratory of Nonlinear Dynamics, Saratov State University,
Saratov,
Russia
Recently the new phenomenon of the locking of the mean switching frequency (MSF) by external periodic force was found [1]. This phenomenon is as follows: there is an interval of noise intensities in which the MSF remains constant and coincides with the frequency of the force. The phenomenon of the locking of the mean switching frequency was proved experimentally by classical model of the Schmitt trigger having noise-induced switching. Qualitatively, the same phenomenon has been observed for the overdamped bistable oscillator.
We investigate the possibility of the realization of the similar
effect in chaotic bistable system without external noise.
In this case the statistical properties of the transitions between states
are exclusively determinated the natural nonlinear dynamics of the system.
The object of
the investigation is the nonautonomous Chua's circuit where there is regim
generalized bistability (attractor Double-Scroll). The random switching
process is investigated numerically via the "two-state" dynamics method. This
process can be characterized by the probability density p(t) of the
switching periods between states and, therefore, by some mean switching
frequency 
. In autonomous Chua's circuit MSF depends on the
two parameters 
and 
. Let us fix parameter 
.
Then the dynamics of the autonomous system is determined by the value of
parameter . The dependences of MSF versus parameter for
different values of amplitudes and frequencies of the external force are
considerated.
In the result of numerical analysis of the nonautonomous Chua's circuit in the "chaos-chaos" type intermittency regime the following conclusions can be made:
- The irregular dependences of the MSF versus parameter
for relatively
large amplitudes of the periodic force are observed as well as it has been
shown in [1]. There is an interval of
the parameter in which MSF is closed to forcing frequency. The size
of the intervals is increased when amplitude and frequency of the force are
rised.
- If one supposes that MSF is equal to the forcing frequency within the bound of some accuracy then we may talk about effect of the locking of the mean switching frequency by external periodic force in a sense introduced in [1].