Networks of Self-Adaptive Dynamical Systems

Rodriguez J, Hongler M-O (2014)
IMA Journal of Applied Mathematics 79(2): 201-240.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Rodriguez, JulioUniBi; Hongler, Max-Olivier
Abstract / Bemerkung
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.
Stichworte
Laplacian matrices; Lyapunov method; networks' adjacency and; ortho-gradient dynamics; mixed canonical-dissipative systems; cycle oscillators; self-adaptive mechanisms; limit
Erscheinungsjahr
2014
Zeitschriftentitel
IMA Journal of Applied Mathematics
Band
79
Ausgabe
2
Seite(n)
201-240
ISSN
0272-4960
eISSN
1464-3634
Page URI
https://pub.uni-bielefeld.de/record/2673577

Zitieren

Rodriguez J, Hongler M-O. Networks of Self-Adaptive Dynamical Systems. IMA Journal of Applied Mathematics. 2014;79(2):201-240.
Rodriguez, J., & Hongler, M. - O. (2014). Networks of Self-Adaptive Dynamical Systems. IMA Journal of Applied Mathematics, 79(2), 201-240. doi:10.1093/imamat/hxs057
Rodriguez, Julio, and Hongler, Max-Olivier. 2014. “Networks of Self-Adaptive Dynamical Systems”. IMA Journal of Applied Mathematics 79 (2): 201-240.
Rodriguez, J., and Hongler, M. - O. (2014). Networks of Self-Adaptive Dynamical Systems. IMA Journal of Applied Mathematics 79, 201-240.
Rodriguez, J., & Hongler, M.-O., 2014. Networks of Self-Adaptive Dynamical Systems. IMA Journal of Applied Mathematics, 79(2), p 201-240.
J. Rodriguez and M.-O. Hongler, “Networks of Self-Adaptive Dynamical Systems”, IMA Journal of Applied Mathematics, vol. 79, 2014, pp. 201-240.
Rodriguez, J., Hongler, M.-O.: Networks of Self-Adaptive Dynamical Systems. IMA Journal of Applied Mathematics. 79, 201-240 (2014).
Rodriguez, Julio, and Hongler, Max-Olivier. “Networks of Self-Adaptive Dynamical Systems”. IMA Journal of Applied Mathematics 79.2 (2014): 201-240.
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