Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium
After the report of chaotic flows with line equilibrium, there has been much attention to systems with uncountable equilibria in the past five years. This work proposes a new system with an infinite number of equilibrium points located on a closed curve. It is worth noting that the new system genera...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/7138971 |
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| _version_ | 1832549687617388544 |
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| author | Xiong Wang Viet-Thanh Pham Christos Volos |
| author_facet | Xiong Wang Viet-Thanh Pham Christos Volos |
| author_sort | Xiong Wang |
| collection | DOAJ |
| description | After the report of chaotic flows with line equilibrium, there has been much attention to systems with uncountable equilibria in the past five years. This work proposes a new system with an infinite number of equilibrium points located on a closed curve. It is worth noting that the new system generates chaotic behavior as well as hidden attractors. Dynamics of the system with closed curve equilibrium have been investigated by using phase portraits, bifurcation diagram, maximal Lyapunov exponents, and Kaplan–York dimension. In addition, we introduce an electronic implementation of the theoretical system to verify its feasibility. Antisynchronization ability of the new system with infinite equilibria is studied by applying an adaptive control. This study suggests that there exist other chaotic systems with uncountable equilibria in need of further investigation. |
| format | Article |
| id | doaj-art-dc6df3051f534fba9472c3cc8457b2e6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-dc6df3051f534fba9472c3cc8457b2e62025-02-03T06:10:51ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/71389717138971Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve EquilibriumXiong Wang0Viet-Thanh Pham1Christos Volos2Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, ChinaSchool of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, VietnamDepartment of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, GreeceAfter the report of chaotic flows with line equilibrium, there has been much attention to systems with uncountable equilibria in the past five years. This work proposes a new system with an infinite number of equilibrium points located on a closed curve. It is worth noting that the new system generates chaotic behavior as well as hidden attractors. Dynamics of the system with closed curve equilibrium have been investigated by using phase portraits, bifurcation diagram, maximal Lyapunov exponents, and Kaplan–York dimension. In addition, we introduce an electronic implementation of the theoretical system to verify its feasibility. Antisynchronization ability of the new system with infinite equilibria is studied by applying an adaptive control. This study suggests that there exist other chaotic systems with uncountable equilibria in need of further investigation.http://dx.doi.org/10.1155/2017/7138971 |
| spellingShingle | Xiong Wang Viet-Thanh Pham Christos Volos Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium Complexity |
| title | Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium |
| title_full | Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium |
| title_fullStr | Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium |
| title_full_unstemmed | Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium |
| title_short | Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium |
| title_sort | dynamics circuit design and synchronization of a new chaotic system with closed curve equilibrium |
| url | http://dx.doi.org/10.1155/2017/7138971 |
| work_keys_str_mv | AT xiongwang dynamicscircuitdesignandsynchronizationofanewchaoticsystemwithclosedcurveequilibrium AT vietthanhpham dynamicscircuitdesignandsynchronizationofanewchaoticsystemwithclosedcurveequilibrium AT christosvolos dynamicscircuitdesignandsynchronizationofanewchaoticsystemwithclosedcurveequilibrium |