On global dynamic behavior of weakly connected cellular nonlinear networks

It is shown that the global dynamics of weakly connected cellular nonlinear networks can be investigated through the joint application of Malkin´s theorem and of the describing function technique. As a case study a one-dimensional array of third order oscillators is considered. Firstly a very accurate analytical expression of the phase deviation equation (i.e. the equation that describes the phase deviation due to the weak coupling) is derived. Then the total number of limit cycles and their stability properties are estimated via the analytical study of the phase deviation equation. We remark that the proposed technique can be applied to a large class of weakly connected nonlinear networks. In particular two-dimensional, space variant and fully connected networks can be dealt with.