Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

2015 ◽  
Vol 25 (04) ◽  
pp. 1550052 ◽  
Author(s):  
J. Kengne
Keyword(s):  
Integrated Circuit ◽  
Nonlinear Dynamical Systems ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Piecewise Linear Approximation ◽  
Transient Chaos ◽  
Frequency Spectra ◽  
Nonlinear Dynamical ◽  
System Parameters ◽  
Coexistence Of Attractors

In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

Multistability Control of Hysteresis and Parallel Bifurcation Branches through a Linear Augmentation Scheme

2019 ◽  
Vol 75 (1) ◽  
pp. 11-21 ◽  
Author(s):  
T. Fonzin Fozin ◽  
G. D. Leutcho ◽  
A. Tchagna Kouanou ◽  
G. B. Tanekou ◽  
R. Kengne ◽  
...  
Keyword(s):  
Coupling Parameter ◽  
Phase Portraits ◽  
Coexisting Attractors ◽  
Nonlinear Dynamical ◽  
Numerical Investigations ◽  
System Parameters ◽  
Chua’S Oscillator ◽  
Control Scheme ◽  
Periodic Attractors ◽  
Basin Of Attractions

AbstractMultistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

Generating Fully Bounded Chaotic Attractors

2011 ◽  
Vol 2 (3) ◽  
pp. 36-42
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

scholarly journals Bifurcations, Hidden Chaos and Control in Fractional Maps

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 879 ◽  
Author(s):  
Adel Ouannas ◽  
Othman Abdullah Almatroud ◽  
Amina Aicha Khennaoui ◽  
Mohammad Mossa Alsawalha ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Discrete Fractional Calculus ◽  
Hidden Attractors ◽  
Nonlinear Dynamical ◽  
Control Schemes ◽  
Stable Equilibria ◽  
And Control

Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.

Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos

1996 ◽  
Vol 118 (3) ◽  
pp. 375-383 ◽  
Author(s):  
R. S. Chancellor ◽  
R. M. Alexander ◽  
S. T. Noah
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Unstable Periodic Orbits ◽  
Bifurcation Diagrams ◽  
Frequency Spectra ◽  
Nonlinear Dynamics And Chaos ◽  
Chaotic Nature ◽  
Parameter Values

A method of detecting parameter changes using analytical and experimental nonlinear dynamics and chaos is applied to a piecewise-linear oscillator. Experimental data show the chaotic nature of the system through phase portraits, Poincare´ maps, frequency spectra and bifurcation diagrams. Unstable periodic orbits were extracted from each chaotic time series obtained from the system with six different parameter values. Movement of the unstable periodic orbits in phase space is used to detect parameter changes in the system.

Action Recognition Based on Motion Representing and Reconstructed Phase Spaces Matching of 3D Joint Positions

2013 ◽  
Vol 333-335 ◽  
pp. 675-679
Author(s):  
Yan Tao Zhao ◽  
Bo Zhang ◽  
Xu Guang Zhang ◽  
Xiao Li Li ◽  
Mei Ling Fu ◽  
...  
Keyword(s):  
Action Recognition ◽  
Human Body ◽  
Nonlinear Dynamical Systems ◽  
Human Action Recognition ◽  
Human Action ◽  
Polar Space ◽  
Phase Portraits ◽  
Nonlinear Dynamical ◽  
Human Pose ◽  
Body Joints

This paper presents an efficient and novel framework for human action recognition based on representing the motion of human body-joints and the theory of nonlinear dynamical systems. Our work is motivated by the pictorial structures model and advances in human pose estimation. Intuitively, a collective understanding of human joints movements can lead to a better representation and understanding of any human action through quantization in the polar space. We use time-delay embedding on the time series resulting of the evolution of human body-joints variables along time to reconstruct phase portraits. Moreover, we train SVM models for action recognition by comparing the distances between trajectories of human body-joints variables within the reconstructed phase portraits. The proposed framework is evaluated on MSR-Action3D dataset and results compared against several state-of-the-art methods.

Real and apparent divergencies in low-frequency spectra of nonlinear dynamical systems

1985 ◽  
Vol 31 (3) ◽  
pp. 1830-1840 ◽  
Author(s):  
A. Ben-Mizrachi ◽  
I. Procaccia ◽  
N. Rosenberg ◽  
A. Schmidt ◽  
H. G. Schuster
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Low Frequency ◽  
Frequency Spectra ◽  
Nonlinear Dynamical

scholarly journals Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ning Wang ◽  
Bocheng Bao ◽  
Tao Jiang ◽  
Mo Chen ◽  
Quan Xu
Keyword(s):  
Chaotic Attractor ◽  
Initial Conditions ◽  
System Model ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Chaotic Oscillator ◽  
Initial Condition ◽  
Bifurcation Diagrams ◽  
System Parameters ◽  
Dynamical Behaviors

This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.

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