scholarly journals Algorithms for Controlling chaos: Application to BVP Oscillator

1993 ◽  
Vol 132 ◽  
pp. 45-45
Author(s):  
S. Rajeskar
Keyword(s):  
Computer Simulations ◽  
Limit Cycles ◽  
Digital Computer ◽  
Chaotic Dynamics ◽  
Van Der Pol Oscillator ◽  
Time Dependent ◽  
Van Der Pol ◽  
Small Magnitude ◽  
Controlling Chaos ◽  
Regular Motion

AbstractWe discuss how chaotic dynamics can be converted into regular motion in Bonhoeffer-van der Pol oscillator. Using a control signal proportional to the actual and desired outputs we study the control of fixed points and limit cycles by making time-dependent perturbations of amplitude of external force. We show the round-off induced periodicity in the digital computer simulations of orbits on chaotic attractor. We illustrate the stabilization of unstable periodic or bits by adding periodic pulses of small magnitude.

Investigation on Dynamics of the Extended Duffing-Van der Pol System

2009 ◽  
Vol 64 (5-6) ◽  
pp. 341-346 ◽  
Author(s):  
Jun Yu ◽  
Jieru Li
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Nonlinear System ◽  
Computer Simulations ◽  
Chaotic Motion ◽  
Dynamical Behaviour ◽  
Higher Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Melnikov Analysis

Abstract The chaotic motion in periodic self-excited oscillators has been extensively investigated through experiments and computer simulations. However, with the advent of the study of chaotic motion by means of strange attractors, Poincar´e map, fractal dimension, it has become necessary to seek for a better understanding of nonlinear system with higher order nonlinear terms. In this paper we consider an extended Duffing-Van der Pol oscillator by introducing a nonlinear quintic term. The dynamical behaviour of the system is investigated by using Melnikov analysis and numerical simulation. The results can help one to understand the essence of given nonlinear system.

On the Existence of Limit Cycles and Relaxation Oscillations in a 3D van der Pol-like Memristor Oscillator

2017 ◽  
Vol 27 (07) ◽  
pp. 1750102
Author(s):  
Marcelo Messias ◽  
Anderson L. Maciel
Keyword(s):  
Phase Space ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Relaxation Oscillator ◽  
Van Der Pol Oscillator ◽  
Relaxation Oscillations ◽  
Van Der Pol ◽  
Piecewise Linear System ◽  
Parameter Values

We study a van der Pol-like memristor oscillator, obtained by substituting a Chua’s diode with an active controlled memristor in a van der Pol oscillator with Chua’s diode. The mathematical model for the studied circuit is given by a three-dimensional piecewise linear system of ordinary differential equations, depending on five parameters. We show that this system has a line of equilibria given by the [Formula: see text]-axis and the phase space [Formula: see text] is foliated by invariant planes transverse to this line, which implies that the dynamics is essentially two-dimensional. We also show that in each of these invariant planes may occur limit cycles and relaxation oscillations (that is, nonsinusoidal repetitive (periodic) solutions), depending on the parameter values. Hence, the oscillator studied here, constructed with a memristor, is also a relaxation oscillator, as the original van der Pol oscillator, although with a main difference: in the case of the memristor oscillator, an infinity of oscillations are produced, one in each invariant plane, depending on the initial condition considered. We also give conditions for the nonexistence of oscillations, depending on the position of the invariant planes in the phase space.

scholarly journals Computer and Hardware Modeling of Periodically Forcedϕ6-Van der Pol Oscillator

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
A. O. Adelakun ◽  
A. N. Njah ◽  
O. I. Olusola ◽  
S. T. Wara
Keyword(s):  
Numerical Simulation ◽  
Chaotic Dynamics ◽  
Random Number ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Secure Communications ◽  
Multiple Time ◽  
Van Der Pol ◽  
Simulation Results ◽  
Good Agreement

Numerical simulation results for the dynamics ofϕ6-systems abound in the literature but their experimental results are yet to be known. This paper presents the chaotic dynamics ofϕ6-Van der Pol oscillator via electronic design, simulation, and hardware implementation. The results obtained are found to be in good agreement with numerical simulation results. The condition for stability of the fixed points is also computed and the method of multiple time scale is used to investigate the dynamical behaviour of the system. Therefore, theϕ6-circuits which have rich dynamics and may have important applications in secure communications, random number generations, cryptography, and so forth have been practically implemented.

BIFURCATION STRUCTURE OF A DRIVEN MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (II): SYMMETRY-BREAKING CRISIS AND INTERMITTENCY

1991 ◽  
Vol 01 (03) ◽  
pp. 711-715 ◽  
Author(s):  
C. EICHWALD ◽  
F. KAISER
Keyword(s):  
Symmetry Breaking ◽  
Limit Cycles ◽  
Critical Exponents ◽  
The Self ◽  
Van Der Pol Oscillator ◽  
Chaotic Attractors ◽  
Bifurcation Structure ◽  
Van Der Pol ◽  
Sustained Oscillations ◽  
Symmetry Properties

Bifurcations in the superharmonic region of a generalized version of the van der Pol oscillator which exhibits three limit cycles are investigated. An external force causes the subsequent breakdown of the self-sustained oscillations. Beyond these series of bifurcations chaotic solutions also exist. They display a symmetry-breaking crisis followed by a type III intermittency transition. The bifurcations are discussed with respect to the symmetry properties of chaotic attractors. The critical exponents connected with the bifurcations offer a scaling which partially contradicts that known from literature. An explanation for this behavior is given.

scholarly journals The van der Pol oscillator under hysteretic control: regular and chaotic dynamics

2019 ◽  
Vol 1368 ◽  
pp. 042030 ◽  
Author(s):  
M E Semenov ◽  
O O Reshetova ◽  
V A Sobolev ◽  
A M Solovyov ◽  
P A Meleshenko ◽  
...  
Keyword(s):  
Chaotic Dynamics ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Hysteretic Control

BIFURCATION STRUCTURE OF A DRIVEN, MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (I): THE SUPERHARMONIC RESONANCE STRUCTURE

1991 ◽  
Vol 01 (02) ◽  
pp. 485-491 ◽  
Author(s):  
F. KAISER ◽  
C. EICHWALD
Keyword(s):  
Limit Cycle ◽  
External Force ◽  
Limit Cycles ◽  
The Self ◽  
Van Der Pol Oscillator ◽  
Resonance Structure ◽  
Bifurcation Structure ◽  
Van Der Pol ◽  
Superharmonic Resonance ◽  
Sustained Oscillations

Bifurcations in the superharmonic region of a generalized version of the van der Pol oscillator which exhibits three limit cycles are investigated. An external force causes the subsequent breakdown of the self-sustained oscillations. Beyond these series of bifurcations chaotic solutions also exist. In this first part we concentrate on a discussion of the bifurcation structure of the system.

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