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.

Mutual Synchronization of Dissipatively Coupled Memristive Self-Oscillators

Background and Objectives: Dynamical systems containing memristive elements, i.e. elements with “memory”, represent a special class of dynamical systems that can be named memristive systems. In memristive systems, the synchronization of oscillations has some features. However, a complete description of these features is still lacking. For the most part, this concerns the synchronization of memristive self-oscillators, both identical and with frequency detuning.

Взаимная синхронизация диссипативно связанных мемристивных генераторов

В работе исследуются особенности полной и фазо-частотной синхронизации в системе двух диссипативно связанных мемристивных генераторов периодических колебаний. Демонстрируются особенности синхронизации, связанные с мемристивным характером взаимодействующих систем. Они заключаются в непрерывной зависимости границ синхронизации (как полной, так и частотной) от начальных условий, в частности, от начального состояния мемристивных элементов двух генераторов.


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.

Chaos in the System of Three Coupled Rotators: from Anosov Dynamics to Hyperbolic Attractor

The work presents an example of a system with chaotic dynamics built of three rotators by modifying a conservative system with hyperbolic Anosov dynamics. Results of a computational study of chaotic dynamics are considered (portraits of attractors, time dependences of the variables, Lyapunov exponents, and spectra) and good correspondence is observed between the dynamics on the attractor of the proposed system with the reduced model, characterized by the Anosov dynamics at appropriately defined energy.

From Anosov’s Dynamics on a Surface of Negative Curvature to Electronic Generator of Robust Chaos

Background and Objectives: Systems with hyperbolic chaos should be of preferable interest due to structural stability (roughness) that implies insensitivity to variation of parameters, manufacturing imperfections, interferences, etc. However, until recently, exclusively formal mathematical examples of this kind of dynamical behavior were known. It makes sense to turn to purposeful constructing the systems with hyperbolic dynamics appealing to tools of physics and electronics.

About Conditionality of Nonlinear Responce of Miogenic Response of Afferent Arteriola for Irregular Self-Sustained Oscillations of Nephron Proximal Pressure

By means of nonlinear dynamics and time series analysis we investigate the possible mechanisms for the onset of chaotic selfsustained dynamics in nephron tubular pressure that is observed experimentally. Our results suggests that the miogenic constriction mechanism of afferent arteriola plays the key role providing the nonlinear response on temporal variation of filtration rate.