Networks of Mixed Canonical-Dissipative Systems and Dynamic Hebbian Learning

Abstract

We study the dynamics of a network consisting of N diffusively coupled, stable-limit-cycle oscillators on which individual frequencies are parametrized by ωk , k = 1, . . . , N. We introduce a learning rule which influences the ωk by driving the system towards a consensual oscillatory state in which all oscillators share a common frequency ωc . We are able to analytically calculate ωc . The network topology strongly affects the relaxation rate but not the ultimate consensual ωc . We report numerical simulations to show the learning mechanisms at work and confirm our theoretical assertions.

Keywords

• mixed canonical-dissipative systems
• diffusive coupling
• Laplacian matrix
• algebraic connec- tivity.