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.
Traveling waves propagation on networks of dynamical systems / Innocenti, Giacomo; Paoletti, P.. - STAMPA. - World Congress, Volume# 18, Part# 1:(2011), pp. 8445-8450. (Intervento presentato al convegno 18th World Congress of the International Federation of Automatic Control tenutosi a Milano (Italy) nel 28/08/2011 - 02/09/2011) [10.3182/20110828-6-IT-1002.02238].
Traveling waves propagation on networks of dynamical systems
INNOCENTI, GIACOMO;
2011
Abstract
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.File | Dimensione | Formato | |
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