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


Attractor

Hyperbolic strange attractors of physically realizable systems

A review of studies aimed on revealing or constructing physical systems with hyperbolic strange attractors, like Plykin attractor and Smale–Williams solenoid, is presented. Examples of iterated maps, differential equations, and simple electronic devices with chaotic dynamics associated with such attractors are presented and discussed. A general principle is considered and illustrated basing on manipulation of phases in alternately excited oscillators and time-delay systems.

Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in context of family of blue sky catastrophes

A new four-dimensional model with quasi-periodic dynamics is suggested. The torus attractor originates via the saddle-node bifurcation, which may be regarded as a member of a bifurcation family embracing different types of blue sky catastrophes. Also the torus birth through the Neimark-Sacker bifurcation occurs in some other region of the parameter space. 

Uniformly hyperbolic attractor in a system based on coupled oscillators with «figure-eight» separatrix

A new autonomous system with chaotic dynamics corresponding to Smale–Williams attractor in Poincare map is introduced. The system is constructed on the basis of the model with «figure-eight» separatrix on the phase plane discussed in former times by Y.I. Neimark. Our system is composed of two Neimark subsystems with generalized coordinates x and y. It is described by the equations with additional terms due to which the system becomes self-oscillating.

Simple electronic chaos generators and their circuit simulation

Topic and aim. The aim of the work is to review circuits of chaos generators, those described in the literature and some original ones, in a unified style basing on circuit simulations with the NI Multisim package, which makes the comparison of the various devices apparent. Investigated models.

Hyperbolic chaos in the Bonhoeffer–van der Pol oscillator with additional delayed feedback and periodically modulated excitation parameter

Topic and aim. The aim of the work is to consider an easy-to-implement system demonstrating the Smale–Williams hyperbolic attractor based on the Bonhoeffer–van der Pol oscillator, alternately manifesting a state of activity or suppression due to periodic modulation of the parameter by an external control signal, and supplemented with a delayed feedback circuit. Investigated models. A mathematical model is formulated as a non-autonomous second-order equation with delay. The scheme of the electronic device that implements this type of chaotic behavior is proposed.

BELYKH ATTRACTOR IN ZASLAVSKY MAP AND ITS TRANSFORMATION UNDER SMOOTHING

If we allow non-smooth or discontinuous functions in definition of an evolution operator for dynamical systems, then situations of quasi-hyperbolic chaotic dynamics often occur like, for example, on attractors in model Lozi map and in Belykh map.

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