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耦合Stuart-Landau振子系统中的广义同步解
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Abstract:
本文研究了耦合Stuart-Landau振子系统的广义同步解，我们利用旋转周期解方法得出了该系统广义同步解的临界条件及分支区域。首先，我们对原系统作线性变换得到标准的Stuart-Landau振子系统，然后我们利用旋转周期解方法得到了变换后系统的完全同步与反同步解分支的临界条件，并获得相应的解的分支图。其次我们利用数值模拟得到变换前系统的广义同步解的分支图，结果表明，尽管系统经历了形式转化，其同步解分支的临界条件与分支图保持不变。所以旋转周期解方法能够处理特殊的同步问题即广义同步问题。
This paper investigates the generalized synchronous solutions of a coupled Stuart-Landau oscillator system. We derived the critical conditions and bifurcation regions for the generalized synchronization solutions of the system by using the rotating periodic solution method. First, we apply a linear transformation to the original system. Then, using the rotating periodic solution method to obtain the critical condition for the bifurcation of synchronous solutions in the transformed system and derive the corresponding synchronization diagram. Next, we perform numerical simulations to generate the bifurcation diagram of generalized synchronous solutions for the original system; the results demonstrate that, despite the formal transformation, both the critical bifurcation conditions and the bifurcation diagram of synchronous solutions remain unchanged. Thus, the rotating periodic solution method is capable of handling special synchronization problems, namely, generalized synchronization.
| [1] | Lodi, M., Sorrentino, F. and Storace, M. (2021) One-Way Dependent Clusters and Stability of Cluster Synchronization in Directed Networks. Nature Communications, 12, Article No. 4073. https://doi.org/10.1038/s41467-021-24363-7 |
| [2] | Ma, M., Lu, Y., Li, Z., Sun, Y. and Wang, C. (2023) Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor. Fractal and Fractional, 7, Article 82. https://doi.org/10.3390/fractalfract7010082 |
| [3] | Marwan, M., Li, F., Ahmad, S. and Wang, N. (2025) Mixed Obstacle Avoidance in Mobile Chaotic Robots with Directional Keypads and Its Non-Identical Generalized Synchronization. Nonlinear Dynamics, 113, 2377-2390. https://doi.org/10.1007/s11071-024-10361-z |
| [4] | Wang, P., Li, X., Wang, N., Li, Y., Shi, K. and Lu, J. (2022) Almost Periodic Synchronization of Quaternion-Valued Fuzzy Cellular Neural Networks with Leakage Delays. Fuzzy Sets and Systems, 426, 46-65. https://doi.org/10.1016/j.fss.2021.02.019 |
| [5] | Shukla, V.K., Joshi, M.C., Mishra, P.K. and Xu, C. (2025) Generalized Synchronization between Coupled Integer, Fractional and Delay Chaotic Systems. Evolving Systems, 16, Article No. 132. https://doi.org/10.1007/s12530-025-09758-x |
| [6] | Shuai, W., Yong, L. and Xue, Y. (2022) Synchronization, Symmetry and Rotating Periodic Solutions in Oscillators with Huygens’ Coupling. Physica D: Nonlinear Phenomena, 434, Article 133208. https://doi.org/10.1016/j.physd.2022.133208 |
| [7] | Wang, S., Li, Y. and Yang, X. (2025) Hopf Bifurcation Theorem of Rotating Periodic Solutions in a Class of Anti-Synchronous Systems. Discrete and Continuous Dynamical Systems, 45, 1150-1179. https://doi.org/10.3934/dcds.2024126 |
| [8] | Wang, S. and Yang, X. (2024) Multi-Type Synchronization for Coupled Van Der Pol Oscillator Systems with Multiple Coupling Modes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34, Article No. 063101. https://doi.org/10.1063/5.0212482 |
| [9] | Bi, Y., Cai, Z. and Wang, S. (2024) Multi-Type Synchronization of Impulsive Coupled Oscillators via Topology Degree. Applications of Mathematics, 69, 185-207. https://doi.org/10.21136/am.2024.0183-23 |
| [10] | Chen, X., Li, F., Liu, X. and Liu, S. (2022) Stability in Star Networks of Identical Stuart-Landau Oscillators with Asymmetric Coupling. Communications in Nonlinear Science and Numerical Simulation, 114, Article 106674. https://doi.org/10.1016/j.cnsns.2022.106674 |
| [11] | Guo, R., Wang, S. and Yang, X. (2025) Synchronization Pattern Recognition Method for Coupled Oscillator Networks on Symmetric Graphs Based on Rotating Periodic Solutions. The European Physical Journal B, 98, Article No. 213. https://doi.org/10.1140/epjb/s10051-025-01057-3 |
