一种有效的方法来估计复杂网络吸引力的领域
IEEE transactions on cybernetics
|August 4, 2025
概括
本研究开发了一种新的方法来估计复杂网络的吸引域 (DOA). 该方法增强了稳定性分析,并且对大规模系统有效.
科学领域:
- 复杂的网络 复杂的网络
- 控制理论 控制理论
- 系统工程 系统工程
背景情况:
- 估计吸引域 (DOA) 对于分析复杂网络的稳定性至关重要.
- 现有的方法往往施加限制性条件或是计算密集型.
研究的目的:
- 开发一种有效和计算效率高的方法来估计复杂网络的DOA.
- 通过放松约束和提高可扩展性来改进现有的DOA估计技术.
主要方法:
- 基于孤立节点属性的复杂网络构建一个二次的利亚普诺夫函数.
- 利用拉普拉斯矩阵创建一个新的莱普诺夫式函数,放松负确定的约束.
- 采用代计算并将问题转换为平方和 (SOS) 多项式网络的编程问题.
主要成果:
- 一种方法直接从一个孤立节点的网络中获得一个网络的DOA最大球形估计.
- 放松了莱普诺夫函数的负确定的导数约束,从而改善了DOA估计.
- 显著减少SOS编程的计算复杂性,使大规模网络的DOA估计成为可能.
结论:
- 拟议的方法提供了一个有效和有效的方法来估计复杂网络中的吸引力领域.
- 这种技术对于大规模的多项式网络特别有效,因为计算复杂性降低了.
- 通过四个说明性示例验证了理论结果.
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