Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity
Joint Authors
Kengne, J.
Kengne, Léandre Kamdjeu
Mboupda Pone, Justin Roger
Kamdem Tagne, Hervé Thierry
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-23
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
Symmetry is an important property found in a large number of nonlinear systems.
The study of chaotic systems with symmetry is well documented.
However, the literature is unfortunately very poor concerning the dynamics of such systems when their symmetry is altered or broken.
In this paper, we investigate the dynamics of a simple jerk system with hyperbolic tangent nonlinearity (Kengne et al., Chaos Solitons, and Fractals, 2017) whose symmetry is broken by adding a constant term modeling an external excitation force.
We demonstrate that the modified system experiences several unusual and striking nonlinear phenomena including coexisting bifurcation branches, hysteretic dynamics, coexisting asymmetric bubbles, critical transitions, and multiple (i.e., up to six) coexisting asymmetric attractors for some suitable ranges of system parameters.
These features are highlighted by exploiting common nonlinear analysis tools such as graphs of largest Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction.
The control of multistability is investigated by using the method of linear augmentation.
We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter.
The theoretical results are confirmed by performing a series of PSpice simulations based on an electronic analogue of the system.
American Psychological Association (APA)
Kengne, Léandre Kamdjeu& Kengne, J.& Mboupda Pone, Justin Roger& Kamdem Tagne, Hervé Thierry. 2020. Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity. Complexity،Vol. 2020, no. 2020, pp.1-24.
https://search.emarefa.net/detail/BIM-1140908
Modern Language Association (MLA)
Kengne, Léandre Kamdjeu…[et al.]. Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity. Complexity No. 2020 (2020), pp.1-24.
https://search.emarefa.net/detail/BIM-1140908
American Medical Association (AMA)
Kengne, Léandre Kamdjeu& Kengne, J.& Mboupda Pone, Justin Roger& Kamdem Tagne, Hervé Thierry. Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity. Complexity. 2020. Vol. 2020, no. 2020, pp.1-24.
https://search.emarefa.net/detail/BIM-1140908
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1140908