arXiv subjects

Vladimir V. Semenov

Publications and source records attributed to Vladimir V. Semenov.

30 records · Page 2Linked to original sources

arXiv2022

Synthesis of memristive one-port circuits with piecewise-smooth characteristics

A generalized approach for the implementation of memristive two-terminal circuits with piesewise-smooth characteristics is proposed on the example of a multifunctional circuit based on a transistor switch. Two versions of the circuit are taken into consideration: an experimental model of the piecewise-smooth memristor (Chua's memristor) and a piecewise-smooth memristive capacitor. Physical experiments are combined with numerical modelling of the discussed circuit models. Thus, it is demonstrated that the considered circuit is a flexible solution for synthesis of a wide range of memristive systems with tuneable characteristics.

nlin.AO↗

arXiv2022

Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria

We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based oscillator. First, all the discussed bifurcation scenarios are considered in the context of systems including Chua's memristor with a piecewise-smooth characteristic. Then the memristor characteristic is changed to a function that is smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration. The presented results are obtained for electronic circuit models, but the considered bifurcation phenomena can be exhibited by systems with a line of equilibria of any nature.

nlin.AO↗

arXiv2021

Subcritical Andronov-Hopf scenario for systems with a line of equilibria

Using numerical simulation methods and analytical approach, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

nlin.AO↗

arXiv2019

Synchronization of periodic self-oscillators interacting via memristor-based coupling

A model of two self-sustained oscillators interacting through memristive coupling is studied. Memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of quasi-harmonic reduction. It is shown that specifics of the memristor nonlinearity results in appearance of infinitely many equilibrium points, which form a line of equilibria in the phase space of the system under study. It is established that possibility to observe the effect of phase locking in the considered system depends both on parameter values and initial conditions. Consequently, boundaries of a synchronization area are determined by the initial conditions. It is demonstrated that addition of a small term into the memristor state equation gives rise to disappearance of the line of equilibria and eliminates the dependence of synchronization on the initial conditions.

nlin.CD↗

arXiv2019

Forced synchronization of an oscillator with a line of equilibria

The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: capture of the phase and frequency of oscillations and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown.

nlin.AO↗

arXiv2018

Dissipative solitons for bistable delayed-feedback systems

We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e. dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that conditions for their appearance is bistability of a nonlinear function and negative character of the delayed feedback. Both dark and bright solitons are identified in numerical simulations and physical electronic experiment showing an excellent qualitative correspondence and proving thereby the robustness of the phenomenon. Along with single spiking solitons, a variety of compound soliton-based structures is obtained in a wide parameter region on the route from the regular dynamics (two quiescent states) to developed spatio-temporal chaos. The number of coexisting soliton-based states is fast growing with delay, which can open new perspectives in the context of information storage.

nlin.AO↗

arXiv2018

Self-oscillation excitation under condition of positive dissipation in a state-dependent potential well

The self-oscillatory dynamics is considered as motion of a particle in a potential field in the presence of dissipation. Described mechanism of self-oscillation excitation is not associated with peculiarities of a dissipation function, but results from properties of a potential, whose shape depends on a system state. Moreover, features of a potential function allow to realize the self-oscillation excitation in a case of the dissipation function being positive at each point of the phase space. The phenomenon is explored both numerically and experimentally on the example of a double-well oscillator with a state-dependent potential and dissipation. After that a simplified single-well model is studied.

nlin.AO↗

arXiv2017

Application of Lagrangian mechanics equations for finding of the minimum distance between smooth submanifolds in N-dimensional Euclidean space -- Part II

The method of finding the minimal distance between smooth non crossing submanifolds in N-dimensional Euclidean space are presented. It based on solution of the equations that describe the dynamics of the pair of material points. The dynamical system can be presented as a natural mechanical system determined by Riemannian geometry on the manifold and chosen potential energy. Such an approach makes it possible to find Lyapunov function of the considered system and to formulates the requirements on the form of potential energy that brings to the convergence of the method.

math.DS↗

arXiv2017

Andronov-Hopf bifurcation with and without parameter in a cubic memristor oscillator with a line of equilibria

The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with bifurcational analysis. It is shown that oscillation excitation has distinctive features of the supercritical Andronov--Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter.

nlin.AO↗

arXiv2017

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

A model of memristor-based Chuas oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational mechanisms of oscillation excitation are explored for different forms of nonlinearity. Hard and soft excitation scenarios have principally different nature. The hard excitation is determined by the memristor piecewise-smooth characteristic and is a result of a border-collision bifurcation. The soft excitation is caused by addition of a smooth nonlinear function and has distinctive features of the supercritical Andronov-Hopf bifurcation. Mechanisms of instability and amplitude limitation are described for both two cases. Numerical modelling and theoretical analysis are combined with experiments on an electronic analog model of the system under study. The issues concerning physical realization of the dynamics of systems with a line of equilibria are considered. The question on whether oscillations in such systems can be classified as the self-sustained oscillations is raised.

nlin.AO↗

arXiv2017

Noise-induced transitions in a double-well excitable oscillator

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase space, which correspond to the self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both two regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function (PDF) caused by noise intensity varying are explained by using the phase space structure of the deterministic system.

nlin.AO↗

arXiv2016

Noise-induced transitions in a double-well oscillator with nonlinear dissipation

We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.

nlin.AO↗