Nonlinear Dynamics of Coupled Arrays of Identical Oscillators

Understanding the complex dynamics of arrays and networks of coupled nonlinear oscillators is one of the major challenges in dynamical systems theory. Considering an array of identical nonlinear oscillators under different couplings, for example global, nonlocal or local, one is interested to know what are the underlying collective dynamical states. The systems can include a variety of physically interesting situations such as neuronal systems, Josephson-junction arrays, chemical and mechanical oscillators. In this talk, I will try to bring out the existence of various collective states, including synchronized, desynchronized, chimera (partially coherent/incoherent) states of different types (like stationary, breathing, amplitude, phase chimeras), clusters, chimera death states and so on in typical nonlinear systems. More interestingly, I will introduce a robust statistical quantitative characterization of these various dynamical states in the form strength of incoherence and discontinuity measure and explain how they can be used in typical systems.