Traveling waves propagation on networks of dynamical systems

Conditions for traveling wave propagation on networks of dynamical systems are investigated by suitably defining a family of ordinary differential equations (ODEs) whose solutions approximate the wave itself with increasing degree of accuracy. A reduced order ODE is considered for computing reference solutions, which are then exploited to prove via implicit function theorem the existence of similar solutions in the original network. A numerical example is included to illustrate the effectiveness of the proposed approach.