Spiral waves occurrence in Cellular Nonlinear Networks

It is well known that nonlinear oscillatory networks are capable of sustaining nonlinear waves and in general spatio-temporal structures. In particular, spiral waves are the most universal form of patterns arising in dissipative media of oscillatory and excitable nature. By focusing on cellular nonlinear networks, whose cells admit of a Lurpsilae description and are linearly connected through weak couplings, the occurrence of spiral waves has been studied through the phase deviation equation obtained by the joint application of the harmonic balance method and Malkinpsilas theorem. Furthermore, a simple condition for verifying the occurrence of spiral waves is derived. Finally the proposed technique is successfully applied to two-dimensional arrays of Chuapsilas circuits in order to prove that such WCONs admit of spiral waves as spatio-temporal patterns.