Kumar Mohit, Gupta Sayan
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India and Complex Systems and Dynamics Group, Indian Institute of Technology Madras, Chennai, 600036, India.
Phys Rev E. 2022 Oct;106(4-1):044310. doi: 10.1103/PhysRevE.106.044310.
Interconnected dynamical systems often transition between states of incoherence and synchronization due to changes in system parameters. These transitions could be continuous (gradual) or explosive (sudden) and may result in failures, which makes determining their nature important. In this study, we abstract dynamical networks as an ensemble of globally coupled Kuramoto-like phase oscillators with frequency-dependent coupling and investigate the mechanisms for transition between incoherent and synchronized dynamics. The characteristics that dictate a continuous or explosive route to synchronization are the distribution of the natural frequencies of the oscillators, quantified by a probability density function g(ω), and the relation between the coupling strength and natural frequency of an oscillator, defined by a frequency-coupling strength correlation function f(ω). Our main results are conditions on f(ω) and g(ω) that result in continuous or explosive routes to synchronization and explain the underlying physics. The analytical developments are validated through numerical examples.
相互连接的动力系统常常会由于系统参数的变化而在非相干态和同步态之间转变。这些转变可能是连续的（渐进的）或爆发性的（突然的），并且可能导致故障，这使得确定它们的性质变得很重要。在本研究中，我们将动力网络抽象为一组具有频率依赖耦合的全局耦合类Kuramoto相位振荡器，并研究非相干动力学和同步动力学之间转变的机制。决定同步的连续或爆发路径的特征是振荡器固有频率的分布，由概率密度函数g(ω)量化，以及振荡器的耦合强度与固有频率之间的关系，由频率 - 耦合强度相关函数f(ω)定义。我们的主要结果是关于f(ω)和g(ω)的条件，这些条件导致同步的连续或爆发路径，并解释了其 underlying 物理原理。通过数值示例验证了分析结果。
