Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System
A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar′e map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically an...
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| Published in | 理论物理通讯：英文版 Vol. 65; no. 9; pp. 297 - 305 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0253-6102 |
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| Summary: | A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar′e map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. |
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| Bibliography: | signal amplitude, signal phase, topological horseshoe, scaling attractor Chun-Lai Li1, Wen Li 1, Jing Zhang 1, Yuan-Xi Xie1, Yi-Bo Zhao2,3 （1College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, China; 2School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China; 3Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Nanjing, Nanjing 210044, China） A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar′e map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. 11-2592/O3 |
| ISSN: | 0253-6102 |