一种由两个Lorenz振荡器非对称双向耦合导出的新型超混沌系统：同步分析与密码学应用
A Novel Hyperchaotic System Derived from Asymmetric Bidirectional Coupling of Two Lorenz Oscillators: Synchronization Analysis and Cryptographic Applications
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中文总结 AI 辅助
本文提出一种由两个Lorenz振荡器非对称双向耦合导出的六维超混沌系统，分析其动力学与同步，并证明在耦合强度满足条件时同步时间可低于0.5秒，优于传统方案，为密码学应用提供基础。
中文摘要 AI 辅助
本文研究了一个通过两个相同Lorenz振荡器的双向非对称扩散耦合得到的六维耦合Lorenz系统。从动力学和同步两个角度对所提出的模型进行了分析。系统地考察了耗散性条件、平衡点、局部稳定性性质和Lyapunov谱。结果表明，存在广泛的混沌和超混沌行为区域，根据耦合参数的不同，最多可有三个正的Lyapunov指数。这些发现为选择保证超混沌动力学同时保持经典Lorenz结构简单性的耦合配置提供了实用框架。\\ 随后发展了基于Lyapunov的同步分析。通过利用从实际系统轨迹而非保守最坏情况估计中获得的有效吸引子界，推导出一个限制性较小的充分同步条件。在经典Lorenz参数下，当$\alpha_1+\alpha_2>15.1$时保证同步。\\ 通过同步时间的参数分析进一步评估了同步性能。数值结果表明，增加耦合强度显著加速了向同步流形的收敛。对于大范围的允许耦合值，实现了低于$0.5$秒的同步时间，而先前报道的基于Lorenz的同步方案通常需要约$5$秒。
英文摘要
This paper investigates a six-dimensional coupled Lorenz system obtained through bidirectional asymmetric diffusive coupling of two identical Lorenz oscillators. The proposed model is analyzed from both dynamical and synchronization perspectives. Dissipativity conditions, equilibrium points, local stability properties, and Lyapunov spectra are systematically examined. The results reveal wide regions of chaotic and hyperchaotic behavior, with up to three positive Lyapunov exponents depending on the coupling parameters. These findings provide a practical framework for selecting coupling configurations that guarantee hyperchaotic dynamics while preserving the simplicity of the classical Lorenz structure. \\ A Lyapunov-based synchronization analysis is then developed. By exploiting effective attractor bounds obtained from the actual system trajectories rather than conservative worst-case estimates, a less restrictive sufficient synchronization condition is derived. Under the classical Lorenz parameters, synchronization is guaranteed for $α_1+α_2>15.1$. \\ The synchronization performance is further evaluated through a parametric analysis of the synchronization time. Numerical results show that increasing the coupling strength significantly accelerates convergence toward the synchronization manifold. For a broad range of admissible coupling values, synchronization times below $0.5$ second are achieved, whereas previously reported Lorenz-based synchronization schemes typically require approximately $5$ seconds.
发表机构
- Science and Technology for Defense Laboratory, Center for Military Research（军事研究中心国防科技与工程实验室）
- Preparatory Institute for Engineering Studies, University of Kairouan（凯鲁万大学工程预科学院）
- Laboratory of Modeling, Mechanics and Production Engineering, National Engineering School of Sfax (ENIS)（萨克斯国立高等工学院建模、力学与生产工程学院）
机构由 AI 辅助整理，请以论文原文为准。
