Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function
In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which disp...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6182183 |
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| author | M. Fouodji Tsotsop J. Kengne G. Kenne Z. Tabekoueng Njitacke |
| author_facet | M. Fouodji Tsotsop J. Kengne G. Kenne Z. Tabekoueng Njitacke |
| author_sort | M. Fouodji Tsotsop |
| collection | DOAJ |
| description | In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions. |
| format | Article |
| id | doaj-art-fb7b9d64d4db4cd684b316d21a3083ec |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-fb7b9d64d4db4cd684b316d21a3083ec2025-08-20T03:25:31ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/61821836182183Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine FunctionM. Fouodji Tsotsop0J. Kengne1G. Kenne2Z. Tabekoueng Njitacke3Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang (Cameroon), Dschang, CameroonUnité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang (Cameroon), Dschang, CameroonUnité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang (Cameroon), Dschang, CameroonUnité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang (Cameroon), Dschang, CameroonIn this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions.http://dx.doi.org/10.1155/2020/6182183 |
| spellingShingle | M. Fouodji Tsotsop J. Kengne G. Kenne Z. Tabekoueng Njitacke Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function Complexity |
| title | Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function |
| title_full | Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function |
| title_fullStr | Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function |
| title_full_unstemmed | Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function |
| title_short | Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function |
| title_sort | coexistence of multiple points limit cycles and strange attractors in a simple autonomous hyperjerk circuit with hyperbolic sine function |
| url | http://dx.doi.org/10.1155/2020/6182183 |
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