Oscillatory behavior in two-dimensional weakly connected cellular nonlinear networks

Two-dimensional layers of oscillatory cellular nonlinear networks are investigated. It is assumed that each cell admits a Lur´e description. In case of weak coupling the main dynamic features of the network are revealed by the phase deviation equation (i.e. the equation that describes the phase deviation due to the weak coupling). In this manuscript a very accurate analytic expression of the phase deviation equation is derived via the joint application of the describing function technique and of Malkin´s theorem. It is shown that the total number of periodic limit cycles with their stability properties can be estimated through the analysis of the phase deviation equation.