Nonlinear Dynamics of Coupled Nonlinear Oscillators: Using of Complex Variables

Abstract We present an asymptotic approach to the analysis of coupled nonlinear oscillators with asymmetric nonlinearity based on the complex representation of the dynamic equations The ideas of the approach are previously given on the example of the system with two degrees of freedom. The special attention is paid to the study of localized normal modes in the chain of weakly coupled nonlinear oscillators. We discuss also certain peculiarities of the localization of excitations in the case of strong coupling between oscillators.