A new four-dimensional two-scroll hyperchaos dynamical system with no rest point, bifurcation analysis, multi-stability, circuit simulation and FPGA design

This paper presents an extended formulation of the basic continuation problem for implicitly defined, embedded manifolds in Rn. The formulation is chosen so as to allow for the arbitrary imposition of additional constraints during continuation and the restriction to selective parametrizations of the corresponding higher-codimension solution manifolds. In particular, the formalism is demonstrated to clearly separate between the essential functionality required of core routines in application-oriented continuation packages, on the one hand, and the functionality provided by auxiliary toolboxes that encode classes of continuation problems and user definitions that narrowly focus on a particular problem implementation, on the other hand. Several examples are chosen to illustrate the formalism and its implementation in the recently developed continuation core package COCO and auxiliary toolboxes, including the continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as the detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations.

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A New Double-Wing Chaotic System With Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation

IEEE Access ◽

10.1109/access.2019.2933456 ◽

2019 ◽

Vol 7 ◽

pp. 115454-115462 ◽

Cited By ~ 20

Author(s):

Aceng Sambas ◽

Sundarapandian Vaidyanathan ◽

Sen Zhang ◽

Yicheng Zeng ◽

Mohamad Afendee Mohamed ◽

...

Keyword(s):

Chaotic System ◽

Bifurcation Analysis ◽

Electronic Circuit ◽

Circuit Simulation ◽

Coexisting Attractors ◽

Electronic Circuit Simulation ◽

Line Equilibrium

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Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4004884 ◽

2011 ◽

Vol 7 (2) ◽

Cited By ~ 4

Author(s):

Yu Guo ◽

Albert C. J. Luo

Keyword(s):

Dynamical System ◽

Bifurcation Analysis ◽

Periodic Motion ◽

Analytical Prediction ◽

Periodic Excitation ◽

Complex Motion ◽

Chaotic Motions ◽

Discontinuous Dynamical System ◽

Mapping Structures ◽

Stability And Bifurcation Analysis

In this paper, complex motions of a ball in the horizontal impact pair with a periodic excitation are studied analytically using the theory of discontinuous dynamical system. Analytical conditions for motion switching caused by impacts are developed, and generic mapping structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic and chaotic motions are given.

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A new multistable hyperjerk dynamical system with self-excited chaotic attractor, its complete synchronisation via backstepping control, circuit simulation and FPGA implementation

International Journal of Modelling Identification and Control ◽

10.1504/ijmic.2020.10036981 ◽

2020 ◽

Vol 35 (3) ◽

pp. 177

Author(s):

Babatunde A. Idowu ◽

Leutcho Gervais Dolvis ◽

Omar Guillén Fernández ◽

Aceng Sambas ◽

Sundarapandian Vaidyanathan ◽

...

Keyword(s):

Dynamical System ◽

Chaotic Attractor ◽

Circuit Simulation ◽

Backstepping Control ◽

Fpga Implementation ◽

Control Circuit

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Stability and Bifurcation Analysis of a Prey–Predator Model

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421500590 ◽

2021 ◽

Vol 31 (04) ◽

pp. 2150059

Author(s):

T. N. Mishra ◽

B. Tiwari

Keyword(s):

Dynamical System ◽

Linear Stability ◽

Bifurcation Analysis ◽

Finsler Space ◽

Second Order ◽

Critical Values ◽

Numerical Examples ◽

Stability And Bifurcation Analysis ◽

Predator Model ◽

The Stability

The purpose of the present paper is to study the stability of a prey–predator model using KCC theory. The KCC theory is based on the assumption that the second-order dynamical system and geodesics equation, in associated Finsler space, are topologically equivalent. The stability (Jacobi stability) based on KCC theory and linear stability of the model are discussed in detail. Further, the effect of parameters on stability and the presence of chaos in the model are investigated. The critical values of bifurcation parameters are found and their effects on the model are investigated. The numerical examples of particular interest are compared to the results of Jacobi stability and linear stability and it is found that Jacobi stability on the basis of KCC theory is global than the linear stability.

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Hopf Bifurcation Analysis and Circuit Simulation of a New Chen Hyper-Chaotic System

2011 Fourth International Workshop on Chaos-Fractals Theories and Applications ◽

10.1109/iwcfta.2011.9 ◽

2011 ◽

Cited By ~ 1

Author(s):

Enzeng Dong ◽

Zhiling Lin ◽

Zaiping Chen ◽

Zengqiang Chen

Keyword(s):

Hopf Bifurcation ◽

Chaotic System ◽

Bifurcation Analysis ◽

Circuit Simulation

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Periodic Motions in the Periodically Forced Oscillator With Multiple Discontinuities

Design Engineering and Computers and Information in Engineering, Parts A and B ◽

10.1115/imece2006-13827 ◽

2006 ◽

Author(s):

Albert C. J. Luo ◽

Mehul T. Patel

Keyword(s):

Dynamical System ◽

Bifurcation Analysis ◽

Analytical Prediction ◽

Periodic Motions ◽

Stability And Bifurcation ◽

Mapping Structures ◽

Forced Oscillator ◽

Stability And Bifurcation Analysis ◽

The Stability

In this paper, the stability and bifurcation of periodic motions in periodically forced oscillator with multiple discontinuities is investigated. The generic mappings are introduced for the analytical prediction of periodic motions. Owing to the multiple discontinuous boundaries, the mapping structures for periodic motions are very complicated, which causes more difficulty to obtain periodic motions in such a dynamical system. The analytical prediction of complex periodic motions is carried out and verified numerically, and the corresponding stability and bifurcation analysis are performed. Due to page limitation, grazing and stick motions and chaos in this system will be investigated further.

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