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

Deterministic Chaos

Excitation of chaotic and stochastic oscillations in different systems

A possible response of both lumped and distributed systems to weak random disturbances of forced character (additive) and the disturbances leading to parametric excitation of oscillations (multiplicative) is presented. It is shown that multiplicative disturbances of a system may cause radical change in its behavior, similar to that occurs in thermodynamically equilibrium systems after second kind phase transitions.

Chaos in the phase dynamics of q­switched van der pol oscillator with additional delayed feedback loop

We present chaos generator based on a van der Pol oscillator with two additional delayed feedback loops. Oscillator alternately enters active and silence stages due to periodic variation of the parameter responsible for the Andronov–Hopf bifurcation. Excitation of the oscillations on each new activity stage is forced by signal resulting from mixing of the first and the second harmonics of signals from previous activity stages, transported through the feedback loops.

Intermittency of type­-I with noise and eyelet intermittency

In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of different sample systems, such as quadratic map, van der Pol oscillator and Rossler system.

Hyperchaos in model nonautonomous system with a cascade excitation transmission through the spectrum

One of the key turbulence theory idea is a cascade energy transmission through the spectrum from large to small scales. It appears that this idea could be used for complex dynamics realization in a different-nature systems even when equations are knowingly differ from hydrodynamical. The system of four van der Pol oscillators is considered in this paper. Chaos generation is realized by cascade excitation transmission from one oscillator to another with frequency doubling.

Controlling chaos in Ikeda system. Symplified discrete map model

Method of controlling chaos in a ring cavity containing a media with cubic phase nonlinearity (Ikeda system) is considered. The proposed method is based on introduction of an additional feedback loop with parameters chosen so that the fundamental frequency components after passing through different feedback loops appear in phase, while the most unstable sidebands appear in antiphase, thus suppressing each other. In the weak dispersion limit a discrete map is derived that is a modification of the well-known Ikeda map.

Controlling chaos in Ikeda system. Spatio–temporal model

The method for controlling chaos in a ring resonator filled 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 Schrodinger Equation with time-delayed boundary condition. Numerical results are presented which confirm 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 LandauStuart oscillators is considered. Subsystems are activated alternately by pairs due to a slow variation of their parameters responsible for the Andronov–Hopf bifurcation. It is shown, that system dynamics depends of coupling type. Different types of phase map (Bernoulli type map) are obtained in Poincare section depending of coupling. Some systems with different type of coupling corresponded to «maximum» and «minimum» chaos are investigated. 

Experimental study of type I intermittency in a generator synchronized with external harmonic signal in the presence of noise

Аn experimental study of statistical properties of type I intermittency in the presence of noise is presented. For the first time an electronic experiment to study periodic oscillations synchronization destruction in case of small detuning in the presence of noise is held. The results are found to be in accordance with theory. 

Phase multistability in an array of period-doubling self­sustained oscillators

Regularities of multistability developments are considered in an array of identical self-sustained oscillators with transition to chaos through period-doubling bifurcations. The used model is chain of diffusivelly coupled Rossler oscillators. The number of coexisting regimes are determined through the cascade of the bifurcations. It is shown that regularities of incresing of attractors are defined be transformation of the phase spectrum duing transition to chaos.

Origin of intermittency in singular hamiltonian systems

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.