Numerical, electronic simulations and experimental analysis of a no-equilibrium point chaotic circuit with offset boosting and partial amplitude control

A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.

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A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

Symmetry ◽

10.3390/sym13061047 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1047

Author(s):

Xuejiao Zhou ◽

Chunbiao Li ◽

Xu Lu ◽

Tengfei Lei ◽

Yibo Zhao

Keyword(s):

Value Function ◽

Initial Conditions ◽

Opposite Polarity ◽

Partial Amplitude ◽

Circuit Implementation ◽

Coexisting Attractors ◽

Amplitude Control ◽

Absolute Value ◽

Numerical Exploration ◽

Discrete Map

An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by two independent coefficients. Symmetrical pairs of coexisting attractors are captured by corresponding initial conditions. Circuit implementation by the platform STM32 is consistent with the numerical exploration and the theoretical observation. This finding is helpful for promoting discrete map application, where amplitude control is realized in an easy way and coexisting symmetrical sequences with opposite polarity are obtained.

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Design and FPGA Verification of Custom-Shaped Chaotic Attractors Using Rotation, Offset Boosting and Amplitude Control

IEEE Transactions on Circuits & Systems II Express Briefs ◽

10.1109/tcsii.2021.3082271 ◽

2021 ◽

pp. 1-1

Author(s):

Wafaa S. Sayed ◽

Merna Roshdy ◽

Lobna A. Said ◽

Ahmed G. Radwan

Keyword(s):

Chaotic Attractors ◽

Amplitude Control ◽

Offset Boosting ◽

Fpga Verification

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Coexisting Multi-Dynamics of a Physical SBT Memristor-Based Chaotic Circuit

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420300438 ◽

2020 ◽

Vol 30 (11) ◽

pp. 2030043

Author(s):

Gang Dou ◽

Hai Yang ◽

Zhenhao Gao ◽

Peng Li ◽

Minglong Dou ◽

...

Keyword(s):

Equilibrium Point ◽

Lyapunov Exponents ◽

Phase Portraits ◽

Circuit Parameter ◽

Bifurcation Diagrams ◽

Chaotic Circuit ◽

Initial State ◽

Stable Point ◽

The Stability ◽

Physical Formula

This paper presents a new physical [Formula: see text] (SBT) memristor-based chaotic circuit. The equilibrium point and the stability of the chaotic circuit are analyzed theoretically. This circuit system exhibits multiple dynamics such as stable point, periodic cycle and chaos by means of Lyapunov exponents spectra, bifurcation diagrams, Poincaré maps and phase portraits, when the initial state or the circuit parameter changes. Specially, the circuit system exhibits coexisting multi-dynamics. This study provides insightful guidance for the design and analysis of physical memristor-based circuits.

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