Reconstitution for interpreting hidden dynamics with stable equilibrium point

Chen, Mo; Wang, Chao; Bao, Han; Ren, Xue; Bao, Bocheng; Xu, Quan

doi:10.1016/j.chaos.2020.110188

Cited by 17 publications

(9 citation statements)

References 49 publications

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“…In recent years, the hidden attractor [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], as a special class of newly defined attractor, has attracted extensive attention from researchers. e attractor that we usually say is also called the self-excited attractor, which is caused by the unstable equilibrium.…”

Section: Multistability and Coexisting Multiple Attractorsmentioning

confidence: 99%

“…Different from the memristive system mentioned above, the nonautonomous FitzHugh-Nagumo (FHN) neuronal circuit was used to solve the problem of critical stability (i.e., hidden attractors) of the system [141]. By using dimensionality reduction modeling, it was proved that the attractors generated by the system were indeed hidden [70,141].…”

Section: Hidden Extreme Multistability Reconstitutionmentioning

confidence: 99%

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Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

2021

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Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.

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Section: Multistability and Coexisting Multiple Attractorsmentioning

confidence: 99%

Section: Hidden Extreme Multistability Reconstitutionmentioning

confidence: 99%

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

2021

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“…In [29,30], the multistability of the series hybrid electric vehicle was investigated. Extreme multistability is a particular case of multistability [31]. In [32], the extreme multistability of a fractional-order oscillator was studied.…”

Section: Introductionmentioning

confidence: 99%

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

Dhinakaran¹,

Alanezi

Natiq³

et al. 2022

Symmetry

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Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

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“…Hidden and self-excited are types of attractors. Many research studies have focused on categorizing dynamical attractors based on them [18][19][20]. A self-excited attractor can be detected easily by observing an unstable equilibrium point in the attractor's basin of attraction.…”

Section: Introductionmentioning

confidence: 99%

A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

Zhang

Vijayakumar²,

Jamal

et al. 2021

Complexity

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Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

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Reconstitution for interpreting hidden dynamics with stable equilibrium point

Cited by 17 publications

References 49 publications

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

A Novel Megastable Oscillator with a Strange Structure of Coexisting Attractors: Design, Analysis, and FPGA Implementation

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