From Geodesic Flow on a Surface of Negative Curvature to Electronic Generator of Robust Chaos

2016 ◽  
Vol 26 (14) ◽  
pp. 1650232 ◽  
Author(s):  
Sergey P. Kuznetsov
Keyword(s):  
Geodesic Flow ◽  
Negative Curvature ◽  
Chaotic Dynamics ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Good Correspondence ◽  
Time Dependencies ◽  
Fourier Spectra ◽  
Model Equations ◽  
Chaos Circuit

Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependencies of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.

Geodesic Flow on Ideal Polyhedra

1997 ◽  
Vol 49 (4) ◽  
pp. 696-707 ◽  
Author(s):  
Charalambos Charitos ◽  
Georgios Tsapogas
Keyword(s):  
Geodesic Flow ◽  
Negative Curvature ◽  
Closed Orbits

AbstractIn this work we study the geodesic flow on n-dimensional ideal polyhedra and establish classical (for manifolds of negative curvature) results concerning the distribution of closed orbits of the flow.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

Conditional measure and flip invariance of Bowen-Margulis and harmonic measures on manifolds of negative curvature

1995 ◽  
Vol 15 (4) ◽  
pp. 807-811 ◽  
Author(s):  
Chengbo Yue
Keyword(s):  
Harmonic Measure ◽  
Geodesic Flow ◽  
Negative Curvature ◽  
Conditional Measure ◽  
Rigidity Result ◽  
Harmonic Measures

AbstractKifer and Ledrappier have asked whether the harmonic measures {νx} on manifolds of negative curvature are equivalent to the conditional measures of the harmonic measure v of the geodesic flow associated with the fibration {SxM}x∈M. We settle this question with a rigidity result. We also clear up the same problem concerning the Patterson-Sullivan measure and the Bowen–Margulis measure.

Stochastic Multiresonance in an Electronic Chaotic Circuit

2014 ◽  
Vol 24 (03) ◽  
pp. 1450027
Author(s):  
Thomas Stemler ◽  
Johannes P. Werner ◽  
Hartmut Benner
Keyword(s):  
Stochastic Resonance ◽  
Linear Response ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Stochastic Systems ◽  
Electronic Circuit ◽  
Chaotic Circuit ◽  
Applied Method

Methods to estimate the amplification by stochastic resonance are tested in an electronic circuit experiment showing chaotic dynamics. We demonstrate that the linear response ansatz used for the estimation in stochastic systems can be also applied to chaotic systems showing crisis induced intermittency. In addition, the applied method explains the mechanism leading to stochastic multiresonance.

TOPOLOGICAL ANALYSIS OF CHAOS IN EQUIVARIANT ELECTRONIC CIRCUITS

1996 ◽  
Vol 06 (12b) ◽  
pp. 2531-2555 ◽  
Author(s):  
C. LETELLIER ◽  
G. GOUESBET ◽  
N.F. RULKOV
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electronic Circuit ◽  
Topological Analysis ◽  
Experimental System ◽  
Electronic Circuits ◽  
Chaotic Oscillations ◽  
Symmetry Properties

Chaotic oscillations in an electronic circuit are studied by recording two time series simultaneously. The chaotic dynamics is characterized by using topological analysis. A comparison with two models is also discussed. Some prescriptions are given in order to take into account the symmetry properties of the experimental system to perform the topological analysis.

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