Dynamical robustness of network of oscillators

Soumen Majhi, Biswambhar Rakshit, Amit Sharma, Jürgen Kurths, Dibakar Ghosh
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Abstract

Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems. Complex networks have proven efficient in elucidating the topological structures of both natural and artificial systems and describing diverse processes occurring within them. Recent advancements have significantly enhanced our understanding of emergent dynamics in complex networks. Among various processes, a substantial body of work explores the dynamical robustness of complex networks, their ability to withstand degradation in network constituents while maintaining collective oscillatory dynamics. Many physical and biological systems experience a decline in dynamic activities due to natural or environmental factors. The impact of such damages on network performance can be significant, and the system's robustness indicates its capability to maintain functionality despite dynamic changes, often termed aging. This review provides a comprehensive overview of notable research examining how networks sustain global oscillation despite increasing inactive dynamical units. We present contemporary research dedicated to the theoretical understanding and enhancement mechanisms of dynamical robustness in complex networks. Our focus includes various network structures and coupling functions, elucidating the persistence of networked systems. We cover system characteristics from heterogeneity in network connectivity to heterogeneity in dynamical units. Finally, we discuss challenges in this field and open areas for future studies.
振荡器网络的动态稳健性
大多数复杂系统都是非线性的,依赖于相互影响的子系统的突发行为,通常以振荡动力学为特征。集体振荡行为对现实世界中许多系统的正常运行至关重要。事实证明,复杂网络可以有效地阐明自然系统和人工系统的拓扑结构,并描述其中发生的各种过程。最近的研究进展极大地增强了我们对复杂网络中突发动力学的理解。在各种过程中,有大量工作探讨了复杂网络的动态鲁棒性,即它们在保持集体振荡动态的同时承受网络成分退化的能力。许多物理和生物系统都会因自然或环境因素而导致动态活动下降。这种破坏对网络性能的影响可能是巨大的,而系统的鲁棒性则表明它有能力在动态变化(通常称为衰老)的情况下保持功能。本综述全面概述了有关网络如何在动态单元失效不断增加的情况下维持全局振荡的著名研究。我们介绍了当代致力于复杂网络动态鲁棒性的理论理解和增强机制的研究。我们的研究重点包括各种网络结构和耦合函数,以阐明网络系统的持久性。我们的研究涵盖了从网络连接的异质性到不对称单元的异质性等系统特征。最后,我们讨论了这一领域的挑战和未来研究的开放领域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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