ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Детерминированный хаос

Controlling chaos in ikeda system spatio–temporal model

The method for controlling chaos in a ring resonator ?lled with a medium with cubic phase nonlinearity (Ikeda system), suggested in [1], is investigated within the framework of a distributed spatio-temporal model described by a Nonlinear Schr? odinger Equation with time-delayed boundary condition. Numerical results are presented which con?rm the capability of the suggested method. For the case of weakly dispersive nonlinear medium, the results are in good agreement with the approximate theory based on the return map [1].

Hyperbolic chaos in a system of nonlinear coupled landau-stuart oscillators

Chaotic dynamics of a system of four nonlinear coupled non-identical Landau-Stuart oscillators is considered. Subsystems are activated alternately by pairs due to aslow variation of their parameters responsible for the Andronov–Hopf bifurcation. It is shown, that system dynamics depends of coupling type. Di?erent types of phase map (Bernoulli type map) are obtained in Poincar? e section depending of coupling. Some systems with di?erent type of coupling corresponded to «maximum» and «minimum» chaos are investigated.

Arnol’d diffusion in a simple nonlinear system: analytical estimations and numerical simulation

We consider the Arnol’d di?usion in a system with 2.5 degrees of freedom along a resonance with an external oscillating ?eld. The analytical estimation of the di?usion coe?cient we made is in a good agreement with numerical results. It’s also shown that both the amplitude of external ?eld and the parameter of weak interaction between two spatial degrees of freedom have an in?uence on Arnol’d di?usion manifestation and its rate.

Mixing and diffusion effect on spatial-temporal dynamics in stochastic lotka–volterra system with discrete phase space

The in?uence of two types of di?usion on dynamics of stochastic lattice Lotka–Volterra model is considered in this work. The simulations were carried out by means of Kinetic Monte-Carlo algorithm. It is shown that the local di?usion considerably changes 75the dynamics of the model and accelerates the interaction processes on the lattice, while the mixing results in appearance of global periodic oscillations. The global oscillations appear due to phenomenon of phase synchronization.

Intermittency concurrence

In this paper we studied intermittent modes in the two-parametric set of onedimensional maps with the neutral unstable point at a phase space boundary. We built the phase diagram in a space of parameters. It de?nes possible transitions to chaos with a parameter change. We showed the unusual mode of the intermittency concurrence. We studied the laminar length distribution function, Lyapunov exponent and topological entropy of this maps set.

The comparative analysis of synchronization by a harmonious and pulse force by the example of lorentz system

The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.  

Application of continuous wavelet transform to analysis of intermittent behavior

Effective method of signals analysis based on the continuous wavelet transform is proposed in this paper. Application of this method to estimation of mean value both of laminar and turbulent phase durations corresponding to different types of intermittent behavior is considered including analysis of time series produced by living systems. It is shown that the proposed method is stable to noise and fluctuations distorting the initial time series.  

Detection of unstable periodical spatio-temporal states of spatial extended chaotic systems dynamics

The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems dynamics is proposed. The application of this method is illustrated by the consideration of the fluid model of Pierce diode which is one of the base system of plasma physics and of microwave electronics.  

Spectral analysis of oscillations in the system of coupled chaotic self-sustained oscillators

Spectra of oscillations in the system of two coupled self-sustained chaotic oscillators are investigated in present work. The relation between spectra and partial effective phase diffusion coefficients is determined. We follow the evolution of spectra and diffusion coefficients from the asynchronous regime to the regime of synchronous chaos. The analogy between spectral characteristics of coupled chaotic oscillators and noisy coupled periodic oscillators is drawn.