intermittency

The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved.

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

In the paper we studied properties of conservative singular maps. It was found that under some conditions the intermittency without chaotic phases can be observed in these maps. The alternative mechanism of the intermittency origin in Hamiltonian singular systems was considered. Its general properties were discussed. We studied special properties of phase space structure in these systems. It is shown that Hamiltonian intermittency can be characterized by zero Lyapunov exponents. It gives us the possibility to classify it as pseoudochaos dynamics.

A modified radio­electronic analog of the nonlinear ring cavity is realized in laboratory. The device represents a special class of oscillations or waves sources. An operation principle of the sources is based on interference amplification of feedback signal by an input signal. A laboratory experiments are performed, the likeness of their results and simulation data is shown. An intermittency, chaos, regular, static modes are detected. A thesis on controlled nonlinearity of dynamical systems is suggested.

The attempt is undertaken to define a class of oscillations or waves sources, the operation principle of which is based on interference amplification of feedback signal by an input signal. The precedent here is the optical Ikeda’s system. The radio­electronic analog of a nonlinear ring interferometer and it modification are offered, the block diagrams and mathematical models are constructed. The computer simulation is performed. An intermittency, chaos, regular, static modes are detected.

In this paper the results of the study of the intermittent behavior taking place near the phase synchronization boundary on the different time scales of the observation are given. It has been shown that below the phase synchronization boundary, in the area of eyelet intermittency there are time scales where the ring intermittency is also observed. In other words, for the certain values of the coupling strength and time scale of observation both types of the intermittent behavior take place simultaneously. In this paper the theory of this type of the intermittent behavior is developed.