Spiral waves in bio-inspired oscillatory media

Spiral waves are the most universal form of patterns arising in dissipative media of oscillatory and excitable nature. By focusing on oscillatory networks, whose cells admit of a Lur´e description and are linearly connected through weak couplings, the occurrence of spiral waves has been studied. In particular, the global dynamic behavior of such networks is investigated through the phase deviation equation obtained by the joint application of the harmonic balance method and Malkin´s theorem. Furthermore, a simple condition for verifying the occurrence of spiral waves is provided.