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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2019, Vol.2019 (2019), p.1-14
Main Author: Gao, Xiaojing
Format: Article
Language:English
Subjects:
Analysis
Bifurcation theory
Chaos theory
Communication
Complexity
Computer simulation
Hopf bifurcation
Investigations
Liapunov exponents
Mathematical models
Mutation
Nonlinearity
Numerical analysis
Parameters
Stability analysis
Time delay systems
Trigonometric functions
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Summary: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).
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/2941835