分析超级网络中的同步动态与它们的单一交互对应之间的关系
Sheida Ansarinasab1, Farnaz Ghassemi1, Fatemeh Parastesh2,3
1Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Chaos (Woodbury, N.Y.)
|October 24, 2025
概括
本研究分析了多种交互类型的复杂超级网络中的同步稳定性. 我们发现非线性相互作用提高了同步性,但增加了能源成本,揭示了实现同步的逆能量-时间关系.
科学领域:
- 复杂系统和网络科学 复杂系统和网络科学
- 非线性动力学和混沌理论
- 统计物理与同步现象
背景情况:
- 超级网络模型系统具有同时的多层交互,对于理解集体行为如同步至关重要.
- 现有的稳定性分析通常依赖于简化假设 (通勤拉普拉西斯,线性相互作用),不代表现实世界的系统.
- 在超级网络中分析同步稳定性,使用非通勤拉普拉斯和混合线性/非线性交互,在计算上具有挑战性.
研究的目的:
- 调查超级网络中的同步动态和稳定性,使用非通勤拉普拉斯和混合扩散合函数.
- 开发一种方法来预测同步稳定性,当直接主稳定性函数 (MSF) 分析是难以解决的.
- 探索拓 (随机,环) 和合类型对同步和能源需求的影响.
主要方法:
- 在随机和环形拓上研究了超级网络与非通行拉普拉斯和线性和非线性扩散合函数.
- 建立了超级网络同步动态及其衍生单个交互对应之间的新型连接.
- 使用洛伦茨振荡器进行数值模拟,以验证理论预测并分析同步区域和能源成本.
主要成果:
- 超级网络表现出由主导合函数影响的中间同步区域.
- 非线性相互作用提高了同步性,但导致了更高的合能量需求.
- 在预同步合能量和实现同步所需的时间之间始终观察到一个反向关系.
结论:
- 该研究提供了一个系统框架,用于分析具有多个交互模式的复杂超级网络中的同步稳定性.
- 开发的方法可以对MSF结构进行定性预测,克服直接分析的局限性.
- 研究结果为现实复杂网络系统中同步的动态,稳定性和能量权衡提供了新的见解.
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