Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity
In the present contribution, an asymmetric central contraction mutation (ACCM) model is proposed to enhance the Ikeda time delay system. The modified Ikeda system model is designed by introducing a superimposed tanh function term into the sine nonlinearity term. Stability and Hopf bifurcation charac...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/2941835 |
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| _version_ | 1832558628420190208 |
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| author | Xiaojing Gao |
| author_facet | Xiaojing Gao |
| author_sort | Xiaojing Gao |
| collection | DOAJ |
| description | In the present contribution, an asymmetric central contraction mutation (ACCM) model is proposed to enhance the Ikeda time delay system. The modified Ikeda system model is designed by introducing a superimposed tanh function term into the sine nonlinearity term. Stability and Hopf bifurcation characteristics of the system are analyzed theoretically. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents spectrum, phase portraits, and two-parameter (2D) largest Lyapunov exponent diagrams are employed to highlight the complex dynamical behaviors exhibited by the enhanced system. The results indicate that the modified system has rich dynamical behaviors including limit cycle, multiscroll hyperchaos, chaos, and hyperchaos. Moreover, as a major outcome of this paper, considering the fragile chaos phenomenon, the ACCM-Ikeda time delay system has better dynamical complexity and larger connected chaotic parameter spaces (connectedness means that there is no stripe corresponding to nonchaotic dynamics embedded in the chaos regions). |
| format | Article |
| id | doaj-art-ed6429b97bbb4448badfec21132e55e7 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ed6429b97bbb4448badfec21132e55e72025-02-03T01:31:57ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/29418352941835Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine NonlinearityXiaojing Gao0School of Computer Science, China University of Geosciences, Building No. 1, North Campus, CUG Lumo Road 388, Wuhan 430074, ChinaIn the present contribution, an asymmetric central contraction mutation (ACCM) model is proposed to enhance the Ikeda time delay system. The modified Ikeda system model is designed by introducing a superimposed tanh function term into the sine nonlinearity term. Stability and Hopf bifurcation characteristics of the system are analyzed theoretically. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents spectrum, phase portraits, and two-parameter (2D) largest Lyapunov exponent diagrams are employed to highlight the complex dynamical behaviors exhibited by the enhanced system. The results indicate that the modified system has rich dynamical behaviors including limit cycle, multiscroll hyperchaos, chaos, and hyperchaos. Moreover, as a major outcome of this paper, considering the fragile chaos phenomenon, the ACCM-Ikeda time delay system has better dynamical complexity and larger connected chaotic parameter spaces (connectedness means that there is no stripe corresponding to nonchaotic dynamics embedded in the chaos regions).http://dx.doi.org/10.1155/2019/2941835 |
| spellingShingle | Xiaojing Gao Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity Complexity |
| title | Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity |
| title_full | Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity |
| title_fullStr | Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity |
| title_full_unstemmed | Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity |
| title_short | Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity |
| title_sort | enhancing ikeda time delay system by breaking the symmetry of sine nonlinearity |
| url | http://dx.doi.org/10.1155/2019/2941835 |
| work_keys_str_mv | AT xiaojinggao enhancingikedatimedelaysystembybreakingthesymmetryofsinenonlinearity |