Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation

Li, Qingdu; Shi-yi, Hu; Song, Tianming; Zeng, Guang Zhao

doi:10.1002/cta.1912

Cited by 115 publications

(49 citation statements)

References 46 publications

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“…24 with an efficient and powerful toolbox in MATLAB called "A toolbox for finding horseshoes in 2D map," 26 which has been successfully applied in many planar maps 27,28 and even three-dimensional maps. 29,30 After we find horseshoe, we verify the four acrossing relations rigorously with the same rigorous computation method in Sec. III.…”

Section: Appendix B: Computer Assisted Verification Of Chaosmentioning

confidence: 99%

New bifurcations in the simplest passive walking model

Song

Yang

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper uncovers several new stable periodic gaits in the simplest passive walking bipedal model proposed in the literature. It is demonstrated that the model has period-3 to period-7 gaits beside the period-1 gaits found by Garcia et al. By simulations, this paper shows that each of these new gaits leads to chaos via period-doubling bifurcation and loses its stability by cyclic-fold bifurcation. This interesting phenomenon suggests a series of new bifurcation scenarios that have not been observed before. To confirm the new gaits and their bifurcations, this paper presents computer assisted proofs on the existence and stability of each periodic gait and its period-doubling gaits with the interval Newton method. To verify that the routes indeed lead to chaos, computer-assisted proofs are also given by means of topological horseshoes theory.

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Section: Appendix B: Computer Assisted Verification Of Chaosmentioning

confidence: 99%

New bifurcations in the simplest passive walking model

Song

Yang

2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…With model (14), the equivalent circuit using analog multipliers and op-amps linked with resistors and/or capacitors [7,8,45] can be handily designed, as shown in Figure 6, which is composed of the linear calculating circuit with three integrating channels and the memristor constitutive relation circuit. In Figure 6, V 1 , V 2 , and V 3 represent three state variables of the capacitor voltages, respectively, and stands for the time constant of the integrators.…”

Section: Controlling Multiple Stable States In Physical Circuitmentioning

confidence: 99%

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

et al. 2018

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This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua's circuit. With the voltage-current model, the initial condition-dependent extreme multistability is explored through analyzing the stability distribution of line equilibrium point and then the coexisting infinitely many attractors are numerically uncovered in such a memristive circuit by the attraction basin and phase portraits. Furthermore, based on the accurate constitutive relation of the memristor emulator, a set of incremental flux-charge describing equations for the memristor-based canonical Chua's circuit are formulated and a dimensionality reduction model is thus established. As a result, the initial condition-dependent dynamics in the voltage-current domain is converted into the system parameter-associated dynamics in the flux-charge domain, which is confirmed by numerical simulations and circuit simulations. Therefore, a controllable strategy for extreme multistability can be expediently implemented, which is greatly significant for seeking chaos-based engineering applications of multistable memristive circuits.

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“…New system (5) is similar to the 4D memristive system in [22], but the function G of the memristive device is a fourth degree polynomial function.…”

Section: New Memristive Hyperchaotic Systemmentioning

confidence: 99%

A Memristive Hyperchaotic System without Equilibrium

Pham

Volos

Gambuzza

2014

The Scientific World Journal

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A new memristive system is presented in this paper. The peculiarity of the model is that it does not display any equilibria and exhibits periodic, chaotic, and also hyperchaotic dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, such as phase portraits, Lyapunov exponents, and Poincaré sections, and circuital implementation confirmed the hyperchaotic dynamic.

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Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation

Cited by 115 publications

References 46 publications

New bifurcations in the simplest passive walking model

New bifurcations in the simplest passive walking model

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

A Memristive Hyperchaotic System without Equilibrium

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