Irregular dynamics of a chain of circle maps with quasiperiodic excitation

An analysis is made of the spatial evolution of quasiperiodic regimes in a chain of coupled circle maps. Mechanisms for the appearance of strange nonchaotic dynamics and the properties of irregular attractors are analyzed. Pis’ma Zh. Tekh. Fiz. 23, 73–79 (April 12, 1997)     

Noise-induced effects in an active medium with periodic boundary conditions

A model of an active medium with periodic boundary conditions in which the elementary cell is represented by a FitzHugh-Nagumo oscillator has been studied. Depending on the system parameters, the elementary cell can occur in either auto-oscillatory or excitable state. In both cases, an autonomous medium in the absence of noise performs sustained oscillations and exhibits the phenomenon of multistability. A method for diagnostics of the character of medium with the aid of external noise is proposed, specific features in behavior of the system near the point of transition from the excitable to auto-oscillatory state are considered, and the phenomena of coherent resonance and noise-induced switching are described.     

Experimental investigation of the evolution of probability distribution in self-sustained oscillators with additive noise

The breakage of a probability distribution characteristic of noise-modulated self-sustained oscillations in nonlinear oscillators with one or one-and-a-half degrees of freedom has been experimentally studied as dependent on the increasing intensity of additive noise.     

Stochastic resonance in a bistable system driven by a chaotic signal

The behavior of a bistable oscillator under the action of a chaotic signal from a Rössler oscillator with a spiral attractor is considered. The influence of the width of the main spectral line of the chaotic drive signal on the signal to noise ratio at the response system’s output has been studied.     

Noise-induced parametric oscillations in nonlinear oscillator

The onset of stochastic oscillations in a nonlinear oscillator with a noise-modulated frequency is considered. It is demonstrated that these oscillations are characterized by the existence of an attractor (i.e., are independent of the initial conditions), but do not exhibit the phenomenon of synchronization typical of self-oscillatory systems.     

Experimental study of the effect of parametric noise on the Andronov–Hopf bifurcation in brusselator

Specific features of the Andronov–Hopf bifurcation in the model of brusselator in the presence of parametric noise are numerically and experimentally studied. Regularities of evolution of the probability distribution with an increase in the noise intensity are typical of the additive and multiplicative effect of the Gaussian white noise. The existence of bifurcation interval corresponding to the gradual transition to the generation regime is experimentally revealed for both additive and multiplicative noise.     

Statistical properties of the instantaneous phase of noisy periodic and chaotic self-sustained oscillations

The statistics of the instantaneous phase of oscillations in dynamic systems with a noisy limit cycle is compared to the statistics of the instantaneous phase of oscillations in dynamic systems with a spiral chaotic attractor. Simulation of the phase dynamics of chaotic self-sustained oscillations by a Wiener process is considered. The results provided by various methods of determination of the instantaneous phase are analyzed.     

Partial synchronization in inhomogeneous autooscillatory media

Investigation of the phenomenon of partial synchronization in a continuous medium with natural frequency detuning depending on a spatial coordinate revealed frequency synchronization cluster formation previously known only in discrete models of distributed systems. The frequency cluster formation and the evolution of the cluster structures depending on the system parameters have been studied.