Work

Dynamics in hybrid complex systems of switches and oscillators

Year: 2013

Type: article

Abstract: While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both oscillators and switches) have received much less attention. We analyze large, hybrid systems of interconnected Kuramoto oscillators and Hopfield switches with positive feedback. In this system, oscillator synchronization promotes switches to turn on. In turn, when switches turn on, they enhance the synchrony of the oscillators to which they are coupled. Depending on the choice of parameters, we find theoretically coexisting stable solutions with either (i) incoherent oscillators and all switches permanently off, (ii) synchronized oscillators and all switches permanently on, or (iii) synchronized oscillators and switches that periodically alternate between the on and off states. Numerical experiments confirm these predictions. We discuss how transitions between these steady state solutions can be onset deterministically through dynamic bifurcations or spontaneously due to finite-size fluctuations.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/1.4822017

Authors: Dane Taylor, Elana J. Fertig, Juan G. Restrepo

Institutions: University of North Carolina at Chapel Hill, Statistical and Applied Mathematical Sciences Institute, University of Colorado Boulder, Johns Hopkins University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Cancer Institute

Awards: G1776710549, Identifying Malignant Cell Signaling from Protein Interactions an Polyomic Data, Adaptation and Percolation in Complex Networks