Izvestiya of Saratov University.
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


Dynamics of the generator with three circuits in the feedback loop. Multistability formation and transition to chaos

Background and Objectives: Studying the dynamical mechanisms of the emergence of nonlinear phenomena that are characteristic for multimode self-oscillating systems consisting of interacting oscillators and an ensemble of passive oscillators or representing active nonlinear systems with complex feedback channels is an important urgent task. The simplest example of a self-oscillating system with a complex feedback is the well-known classical van der Pol oscillator with an additional linear oscillatory circuit included in the feedback channel.


В работе рассмотрен кольцевой генератор с тремя линейными колебательными контурами в цепи обратной связи и нелинейным усилителем. Выведены уравнения генератора, представлены результаты численного моделирования. Построены карты характерных режимов, описаны результаты бифуркационного анализа. Установлено, что добавление колебательных контуров в цепь обратной связи классического генератора Ван дер Поля приводит к появлению квазипериодических и хаотических режимов, к появлению мультистабильности.

Influence of the Co-Phase Harmonis Excitation on the Dynamics of the Two Coupled Period Doubling Systems

The system of two coupled maps under in-phase harmonic forcing is investigated numerically. By calculating of the lyapunov exponent spectrum the structure of control parameters space is investigated, the existence regions of the various multistable states are presented, the structure of the basins of attraction is studed.

Complex Waveforms and Synchronization in Functional Model of Vascular Nephron Tree

We suggest functional model that qualitatively describes oscillatory processes in renal autoregulation. Our model consists of ensemble of two-mode oscillators that are coupled by means of two different pathways. The above coupling pathways count both the geometry of ensemble (tree-like structure or local interaction) and the specific action of individual oscillator (energy distribution netrwork or diffusive coupling). We study the typical operating regimes of suggested model as well as transitions between them.

Complex Dynamics and Chaos in the Rabinovich – Fabrikant Model

Background and Objectives: In the work we consider a finitedimensional three-mode model of the nonlinear parabolic equation. It was proposed in 1979 by M. I. Rabinovich and A. L. Fabrikant. It describes the stochasticity arising from the modulation instability in a non-equilibrium dissipative medium with a spectrally narrow amplification increment. The Rabinovich – Fabrikant system presents some extremely rich dynamics die to the third-order nonlinearities presented in the equations. The considered system is universal.