Dynamics in Co-evolving Networks of Active Elements

Takuma Tanaka¹, Takaaki Aoki² and Toshio Aoyagi^2,3*

¹Graduate School of Medicine, Kyoto University, Kyoto 606-8501, Japan
²Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
³JST, CREST, Japan
*E-mail address: aoyagi@acs.i.kyoto-u.ac.jp

(Received November 29, 2008; Accepted January 20, 2009)

Abstract. We investigate the co-evolving dynamics in a weighted network of various dynamical elements, in which the state of the elements at the nodes and the weights of the links interact with each other. First, we examine the network of phase oscillators with various local, bottom-up rules for the weight of the link, and next investigate the recurrent networks of neurons with the global, top-down learning rule of an extension of the infomax principle. In both cases, some interesting properties of emergent dynamical patterns are found and characterized by mutual information.

Keywords: Complex Network, Phase Oscillator, Nonlinear Dynamics, Recurrent Infomax