Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes

2011 ◽  
Vol 240 (11) ◽  
pp. 903-912 ◽  
Author(s):  
Naohiko Inaba ◽  
Yoshifumi Nishio ◽  
Tetsuro Endo
Keyword(s):  
Torus Breakdown

scholarly journals ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR

2008 ◽  
Vol 18 (04) ◽  
pp. 1051-1068 ◽  
Author(s):  
MUNEHISA SEKIKAWA ◽  
NAOHIKO INABA ◽  
TAKASHI TSUBOUCHI ◽  
KAZUYUKI AIHARA
Keyword(s):  
Bifurcation Diagram ◽  
Van Der Pol Oscillator ◽  
Circle Map ◽  
Bifurcation Structure ◽  
Van Der Pol ◽  
One Dimensional ◽  
Implicit Equations ◽  
Periodic State ◽  
Torus Breakdown ◽  
Theoretical Results

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered.In this case, the Poincaré map is constructed as a one-dimensional map: a circle map. The parameter boundary between a torus-generating region where the circle map is a diffeomorphism and a chaos-generating region where the circle map has extrema is derived explicitly, without solving the implicit equations, by adopting some novel ideas. On the bifurcation diagram, intermittency and a saddle-node bifurcation from the periodic state to the quasi-periodic state can be exactly distinguished. Laboratory experiment is also carried out and theoretical results are verified.

Chaos via torus breakdown

1987 ◽  
Vol 34 (3) ◽  
pp. 240-253 ◽  
Author(s):  
T. Matsumoto ◽  
L. Chua ◽  
R. Tokunaga
Keyword(s):  
Torus Breakdown

ENRICHED DYNAMICS OF A SIMPLE NONLINEAR NONAUTONOMOUS PARALLEL LCR CIRCUIT

2009 ◽  
Vol 19 (07) ◽  
pp. 2347-2358 ◽  
Author(s):  
I. MANIMEHAN ◽  
K. THAMILMARAN ◽  
P. PHILOMINATHAN
Keyword(s):  
Period Doubling ◽  
Nonlinear Element ◽  
Chaotic Oscillator ◽  
Passive Components ◽  
Op Amp ◽  
Rich Variety ◽  
Analytical Results ◽  
Farey Sequences ◽  
Torus Breakdown ◽  
Junction Diode

We present the results of a very simple nonlinear nonautonomous parallel LCR circuit which exhibits a rich variety of bifurcations and chaos. This simple experimental chaotic oscillator is made up of a few passive components and a uniquely designed nonlinear element comprising of a junction diode and Op-amp based negative conductor. The system exhibits a rich dynamics such as chaos via torus breakdown, period-doubling, period three-doubling, period-adding, Farey sequences, etc., and the results of the investigation are vividly presented along with experimental, numerical and analytical evidences. The laboratory experimental outcomes are in agreement with the numerical and analytical results.

Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Nataliya V. Stankevich ◽  
Natalya A. Shchegoleva ◽  
Igor R. Sataev ◽  
Alexander P. Kuznetsov
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Three Dimensional ◽  
Parameter Plane ◽  
Poincare Section ◽  
Dimensional Torus ◽  
Typical Structure ◽  
Periodic Oscillations ◽  
Torus Breakdown ◽  
Periodic Dynamics

Abstract Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincaré section, we have shown destruction of three-frequency torus.

scholarly journals A physical memristor based Muthuswamy–Chua–Ginoux system

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jean-Marc Ginoux ◽  
Bharathwaj Muthuswamy ◽  
Riccardo Meucci ◽  
Stefano Euzzor ◽  
Angelo Di Garbo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Mathematical Analysis ◽  
Three Dimensional ◽  
Memristive Device ◽  
Nonlinear Resistor ◽  
Numerical Investigations ◽  
Double Spiral ◽  
Torus Breakdown ◽  
Autonomous Dynamical System

Abstract In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear “locally active” memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy–Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a “double spiral attractor”.

scholarly journals Torus Breakdown in a Uni Junction Memristor

2018 ◽  
Author(s):  
Jean-Marc Ginoux ◽  
Riccardo Meucci ◽  
Stefano Euzzor
Keyword(s):  
Torus Breakdown

Bifurcations of quasi-periodic dynamics: torus breakdown

2013 ◽  
Vol 65 (6) ◽  
pp. 1053-1076 ◽  
Author(s):  
Taoufik Bakri ◽  
Ferdinand Verhulst
Keyword(s):  
Torus Breakdown ◽  
Periodic Dynamics

Strange Nonchaotic Attractors via Torus Breakdown

1997 ◽  
Vol 07 (06) ◽  
pp. 1425-1430 ◽  
Author(s):  
Zhiwen Zhu ◽  
Zhong Liu
Keyword(s):  
Lyapunov Exponent ◽  
Logistic Map ◽  
Period Doubling ◽  
System Parameters ◽  
Torus Breakdown ◽  
Strange Nonchaotic Attractors

In this paper, we examine the quasiperiodically driven logistic map and discuss a mechanism for the development of strange nonchaotic attractors. It is shown that the attractors can be created from two-frequency torus breakdown. We find that the torus does not undergo period-doubling cascade as usual as system parameters vary, instead, the torus curve becomes extremely wrinkled, loses its smoothness and finally becomes fractal. However the Lyapunov exponent remains negative during the process. The mechanism can be used to explain the onset of strange nonchaotic behaviors in a class of systems.

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