https://doi.org/10.1140/epjb/e2016-70465-y
Regular Article
Topological stabilization for synchronized dynamics on networks
1 Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Firenze, via S. Marta 3, 50139 Florence, Italy
2 Dipartimento di Fisica e Astronomia and CSDC, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
3 INFN Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
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e-mail: giuliacencetti@gmail.com
Received: 4 August 2016
Received in final form: 20 October 2016
Published online: 16 January 2017
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017
