Dynamical analysis and multistability in autonomous hyperchaotic oscillator with experimental verification

In this contribution, a modified oscillator of Tamasevicius et al. (Electron Lett 33:542–544, 1997 ) (referred to as the mTCMNL oscillator hereafter) is introduced with antiparallel diodes as nonlinear elements. The model is described by a continuous time of four-dimensional autonomous system with h...

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Bibliographic Details
Published in:Nonlinear dynamics 2018-07, Vol.93 (2), p.653-669
Main Authors: Fozin Fonzin, T., Kengne, J., Pelap, F. B.
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Chaos theory
Circuits
Classical Mechanics
Continuous time systems
Control
Diodes
Dynamical Systems
Engineering
Frequency spectrum
Liapunov exponents
Mathematical models
Mechanical Engineering
Nonlinearity
Numerical analysis
Original Paper
Parameters
Toruses
Vibration
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Summary:In this contribution, a modified oscillator of Tamasevicius et al. (Electron Lett 33:542–544, 1997 ) (referred to as the mTCMNL oscillator hereafter) is introduced with antiparallel diodes as nonlinear elements. The model is described by a continuous time of four-dimensional autonomous system with hyperbolic sine nonlinearity based on Shockley diode model. Various methods for characterizing chaos/hyperchaos including bifurcation diagrams, Lyapunov exponents spectrum, frequency spectra, phase portraits, Poincaré sections and two parameter Lyapunov exponents diagrams are exploited to point out the rich dynamical behaviors in the model. Numerical results indicate that the system displays extremely rich dynamical behaviors including periodic windows, torus, chaotic and hyperchaotic oscillations. One of the main findings of this work is the presence of a region in the parameter space in which the mTCMNL experiences hysteretic behaviors. This later singularity/phenomenon is marked by the coexistence of multiple attractors (i.e., coexistence of asymmetric pair of periodic, torus and chaotic attractors with symmetric periodic, torus and chaotic attractors), for the same parameters settings. Basins of attractions of various competing attractors depicts symmetric complex basin boundaries, thus suggesting possible jumps between coexisting solutions (i.e., asymmetric pair of attractors with symmetric one) in experiments. A predominant route to chaos/hyperchaos observed in the system for different system parameters is the Afraimovich–Shilnikov scenario with tiny periodic regions. Experimental results from real-time circuit implementation are in good agreement with numerical analysis.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4216-z