Networks of Self-Adaptive Dynamical Systems
We discuss the adaptive behaviour of a collection of heterogeneous dynamical systems interacting via a weighted network. At each vertex, the network is endowed with a dynamical system with individual (initially different) control parameters governing the local dynamics. We then implement a class of network interactions which generates a self-adaptive behaviour, driving all local dynamics to adopt a set of consensual values for their local parameters. While for ordinary synchronization each individual dynamical system is restored to its original dynamics once network interactions are removed, here the consensual values of control parameters are definitively acquired—even if interactions are removed. For a wide class of dynamical systems, we show analytically how such a plastic and self-adaptive training of control parameters can be realized. We base our study on local dynamics characterized by dissipative ortho-gradient vector fields encompassing a vast class of attractors (in particular limit cycles). The forces generated by the coupling network are derived from a generalized potential. A set of numerical experiments enables us to observe the transient dynamics and corroborate the analytical results obtained.
Keywords: Ortho-gradient dynamics - Limit cycles oscillators - self-adaptive mechanisms - adajacency and Laplacian matrices - ; ortho-gradient dynamics ; mixed canonical-dissipative systems ; limit cycle oscillators ; self-adaptive mechanisms ; networks' adjacency and Laplacian matrices ; Lyapunov method
Record created on 2012-09-14, modified on 2016-08-09