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

Deterministic Chaos

Hyperchaos in a system with delayed feedback loop based on Q-switched van der Pol oscillator

We present a way to realize hyperchaotic behavior for a system based on Q-switched van der Pol oscillator with non-linear signal transformation in the delayed feedback loop. The results of numerical studies are discussed: time dependences of variables, attractor portraits, Lyapunov exponents, and power spectrum. 

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

The influence of two types of diffusion 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 diffusion considerably changes the 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.

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

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

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 defines 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.

Investigation of structure of invariant density for Renyi map by Gauss method

It is shown that the structure of the invariant density for Renyi map xn+1 = = βxn mod 1, (1 < β < 2) may be clarified by action of the Perron–Frobenius operator on the uniform distribution. The invariant density is presented by finite linear combination of characteristic functions defined on the unit interval according to special rule. Some algebraic equations with entire coefficients are formulated for parameter β corresponding values definition.

Lyapunov exponents in the Henon–Heiles problem

By the way of combined integrating of the motion and variation equations we calculated the maximal characteristic Lyapunov exponents in the wide limits of energy and time for the Henon–Heiles problem. It follows from the fitting procedure that the best approximate function is the exponential one with the parameter values, which are different from the earlier obtained parameter values (Benettin et al.).

Lorenz attractor in flows of simple shift

In the frame of a model given before for simulation of chaotic dynamics of continuum medium the Lorenz attractor is represented. The simulation is given with the help of the structures that define the geometry of a fiber bundle associated with 3-dimensional regime of velocity pulsations. Lorenz dynamics appears as time dependence of pulsations along the lines of average flow.

Chaotic modes of asymmetric circular billiard with beams reflection and refraction

The paper studies the chaotic dynamics in circular asymmetric billiard with beams reflection and refraction. Phase dynamics is characterized by a variety of dynamics modes, which is connected with the effect of traditional chaotization mechanisms as well as with the complicacy of allowable motion laws. In the multisheet symmetric phase space, the circular billiard reconstructions have been analysed its asymmetry degrees changes. 

Chaotic RF generator based on oscillator with 2.5 degrees of freedom

Chaotic RF generator with bipolar transistor is proposed. Mathematical model of  the generator, oscillator with 2.5 degrees of freedom, is investigated. Generator dynamics is analyzed with Advanced Design System (ADS) software using parameters of a real transistor, properties of the board substrate are taken into account by simulation. ADS simulation results are compared with experimental data.

Generation of chaotic oscillations in experimental scheme of three cascade-coupled phase systems

Results of experimental investigation of chaotic dynamics of the ensemble of three cascade-coupled phase systems (phase-locked loops) are presented. The possibility of dynamical regimes control by means of coupling parameters changing without changing of inner parameters of elements is demonstrated. Spectral and correlation properties of different chaotic regimes are presented. It is shown, that excitation of chaotically modulated oscillation is possible in wide and homogeneous domains of system parameters.