|
|
二维耦合映射系统中的吸引域和冒泡吸引盆
|
Abstract:
混沌同步问题在多个领域都有重要的应用。比如：卫星运动中的混沌同步和反同步问题，分数阶金融系统中的混沌同步问题，不确定混沌系统的自适应同步问题。本文以二维耦合映射系统为例，讨论了混沌同步状态的弱稳定性，冒泡吸引盆的形成。同时利用临界曲线构造吸引域，分析吸引域在局部和全局冒泡出现中的作用。
Chaotic Synchronization has significant applications in many fields. Examples include chaotic synchronization and desynchronization in the motion of satellites, chaotic synchronization in fractional order financial systems, and adaptive synchronization in uncertain chaotic systems. The purpose of this paper is to discuss the weak stability of chaotic synchronization and the formation of riddled basins using the two-dimensional coupled mapping system. The critical curve is simultaneously used to construct the attraction domain, and the role of the attraction domain in the emergence of local and global riddling is analysed.
| [1] | Rulkov, N.F. (1996) Images of Synchronized Chaos: Experiments with Circuits. Chaos: An Interdisciplinary Journal of Nonlinear Science, 6, 262-279. https://doi.org/10.1063/1.166174 |
| [2] | Fujisaka, H. and Yamada, T. (1983) Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. Progress of Theoretical Physics, 69, 32-47. https://doi.org/10.1143/PTP.69.32 |
| [3] | Zhou, L., You, Z. and Tang, Y. (2021) A New Chaotic System with Nested Coexisting Multiple Attractors and Riddled Basins. Chaos, Solitons & Fractals, 148, Article 111057. https://doi.org/10.1016/j.chaos.2021.111057 |
| [4] | Ashwin, P., Buescu, J. and Stewart, I. (1996) From Attractor to Chaotic Saddle: A Tale of Transverse Instability. Nonlinearity, 9, Article 703. https://doi.org/10.1088/0951-7715/9/3/006 |
| [5] | Lai, Y.C., Grebogi, C., Yorke, J.A., et al. (1996) Riddling Bifurcation in Chaotic Dynamical Systems. Physical Review Letters, 77, Article 55. https://doi.org/10.1103/PhysRevLett.77.55 |
| [6] | Cao, Y. (2004) A Note about Milnor Attractor and Riddled Basin. Chaos, Solitons & Fractals, 19, 759-764. https://doi.org/10.1016/S0960-0779(03)00205-4 |
| [7] | Rabiee, M., Ghane, F.H., Zaj, M., et al. (2022) The Occurrence of Riddled Basins and Blowout Bifurcations in a Parametric Nonlinear System. Physica D: Nonlinear Phenomena, 435, Article 133291. https://doi.org/10.1016/j.physd.2022.133291 |
| [8] | Maistrenko, Y.L., Maistrenko, V.L., Popovich, A., et al. (1998) Transverse Instability and Riddled Basins in a System of Two Coupled Logistic Maps. Physical Review E, 57, Article 2713. https://doi.org/10.1103/PhysRevE.57.2713 |
| [9] | Bischi, G.I., Mammana, C. and Gardini, L. (2000) Multistability and Cyclic Attractors in Duopoly Games. Chaos, Solitons & Fractals, 11, 543-564. https://doi.org/10.1016/S0960-0779(98)00130-1 |
| [10] | Abraham, R., Mira, C. and Gardini, L. (1997) Chaos in Discrete Dynamical Systems. Telos. https://doi.org/10.1007/978-1-4612-1936-1 |
