Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/127404 |
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| _version_ | 1832549356582993920 |
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| author | Jie Ran Yu-Qin Li Shao-Juan Ma Juan Wu |
| author_facet | Jie Ran Yu-Qin Li Shao-Juan Ma Juan Wu |
| author_sort | Jie Ran |
| collection | DOAJ |
| description | The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations. |
| format | Article |
| id | doaj-art-15d96c50c6084f2191843b04e87bde61 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-15d96c50c6084f2191843b04e87bde612025-02-03T06:11:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/127404127404Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic SystemJie Ran0Yu-Qin Li1Shao-Juan Ma2Juan Wu3Institute of Mathematics and Computer Science, Zunyi Normal University, Zunyi 563000, ChinaDepartment of Basic Education, Business School of Guizhou University of Finance and Economics, Huishui 550600, ChinaSchool of Mathematics and Information Science, North University of Nationalities, Yinchuan 750021, ChinaSchool of Mathematics and Information Science, North University of Nationalities, Yinchuan 750021, ChinaThe dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.http://dx.doi.org/10.1155/2015/127404 |
| spellingShingle | Jie Ran Yu-Qin Li Shao-Juan Ma Juan Wu Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System Discrete Dynamics in Nature and Society |
| title | Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System |
| title_full | Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System |
| title_fullStr | Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System |
| title_full_unstemmed | Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System |
| title_short | Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System |
| title_sort | hopf bifurcation analysis for a stochastic discrete time hyperchaotic system |
| url | http://dx.doi.org/10.1155/2015/127404 |
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