Design of bio-inspired network models for spatio-temporal pattern identification

Many mathematical models have been proposed to describe systems that present spatio-temporal patterns. Most of them are mainly phase models, where each oscillating cell is characterized in terms of a sole phase variable. It is well known that under suitable assumptions the global dynamics of networks composed by oscillators with weak connections can be investigated through phase models. In particular, the joint application of Malkin´s Theorem and the describing function technique allows one to obtain an analytical approximation of the phase deviation equation for weakly connected networks that admit of a Lur´e representation. The aim of this manuscript is to provide a method for identifying the conditions under which weakly connected oscillatory systems exhibit given spatio-temporal patterns and to exploit the results for designing the corresponding networks.