Publication

Abstract : Summary. Nonlinear Normal Modes (NNMs), defined as two dimensional invariant manifolds in state space, have emerged as powerful analytical tools for the study of nonlinear systems. This work presents a novel approach to the study of synchronisation dynamics in mutually coupled van der Pol oscillators using the concept of NNMs. Shaw and Pierre’s method is used to arrive at the NNMs as a two dimensional manifold parameterised by the displacement and velocity of the first oscillator. It is shown that because of the synchronising property of the system the invariant manifold reduces to a one-dimensional closed curve which remains a subset of the two-dimensional manifold calculated by NNM computation. This is shown to be true for both the oscillating modes of the system which corresponds to in-phase and out of phase synchronisation. It is also shown that the one-dimensional invariant manifold coincides with the synchronised limit cycle of the system for both modes. The NNMs are further used to decouple the governing equations. The decoupled equations which capture the modal dynamics retain the form of single van der Pol equation after removal of insignificant terms. This suggests a novel approach to the study of in-phase and out of phase synchronisation using these equations.