Department of Mathematics, National Institute of Technology, Durgapur 713209, India.
Dr. B. C. Roy Engineering College, Durgapur 713206, India.
Chaos. 2019 Jan;29(1):013112. doi: 10.1063/1.5051535.
We investigate different emergent dynamics, namely, oscillation quenching and revival of oscillation, in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory state (OS), we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states from the homogeneous steady state sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state, i.e., OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS), and (3) Emergence of the OD state from the oscillatory state (OS) without passing through AD, i.e., OS-OD. The dynamics of each node in the network is assumed to be governed either by the identical limit cycle Stuart-Landau system or by the chaotic Rössler system. Based on clustering behavior observed in the oscillatory network, we derive a reduced low-dimensional model of the large network. Using the reduced model, we investigate the effect of time delay on these transitions and demarcate OS, AD, and OD regimes in the parameter space. We also explore and characterize the bifurcation transitions present in both systems. The generic behavior of the low dimensional model and full network is found to match satisfactorily.
我们研究了全局同型振子网络在对称破缺的局部排斥时滞相互作用下的扩散（正）时滞耦合中的不同涌现动力学，即振荡猝灭和振荡恢复。从振荡状态（OS）开始，我们在参数空间中系统地识别出三种类型的相变现象：（1）系统可能从均匀稳定状态达到非均匀稳定状态，有时称为从幅度死亡（AD）到振荡死亡（OD）状态的转变，即 OS-AD-OD 场景；（2）从 AD 状态恢复振荡（OS），即 OS-AD-OS；（3）振荡状态（OS）直接进入 OD 状态，而不经过 AD，即 OS-OD。网络中每个节点的动力学假设由相同的极限环 Stuart-Landau 系统或混沌 Rössler 系统控制。基于在振荡网络中观察到的聚类行为，我们推导出大网络的简化低维模型。使用简化模型，我们研究了时滞对这些相变的影响，并在参数空间中划分 OS、AD 和 OD 区域。我们还探索并描述了两个系统中存在的分岔跃迁。发现低维模型和全网络的一般行为非常吻合。
