Traveling waves in one-dimensional networks of dynamical systems

Propagation of traveling waves along one dimensional networks of identical dynamical systems is analysed by suitably defining a family of ordinary differential equations (ODEs) that describes the traveling wave itself. An ODE of reduced order is derived for computing reference solutions, which are then exploited to prove via implicit function theorem the existence of similar solutions in the original network. An example is included to illustrate the effectiveness of the proposed approach.