Punetha Nirmal, Ramaswamy Ramakrishna, Atay Fatihcan M
Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042906. doi: 10.1103/PhysRevE.91.042906. Epub 2015 Apr 10.
We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or π radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rössler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.
我们研究具有一般非线性耦合和分布式时间延迟的二分相位振子网络中的同步。结果表明，会出现锁相解，其中每个分区中的振子彼此之间完全同步，但与另一个分区可能存在相位差，该相位差必定为零或π弧度。获得了两种类型解的稳定性的解析条件，并明确计算了解分支，揭示了网络可以有多个共存的稳定解。随着平均延迟值的增加，系统表现出滞后、相位翻转、最终状态敏感性以及一种极端形式的多稳定性，即具有不同频率的稳定同相和反相同步解的数量无界增长。该理论应用于Landau-Stuart和Rössler振子网络，并表明在适当的参数范围内能准确预测同相和反相同步行为。
