2016/08/17 by Zalman Balanov, Balanov, Zalman, Edward Hooton +7
Computer Science · Mathematics · Physics and Astronomy · #34H15 (Primary) #34K20 (Secondary) #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #math.DS #math.OC #msc:34H15 #msc:34K20
paper · pdf · doi:10.48550/arxiv.1608.04884
openalex publication_date 2016/08/17 · arxiv created 2016/08/19 · arxiv updated 2016/08/22 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28
Pyragas time delayed feedback control has proven itself as an effective tool to non-invasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings and applied to stabilize branches of small periodic solutions in systems of symmetrically coupled Landau oscillators near a Hopf bifurcation point. The form of the control ensures the non-invasiveness property, hence reducing the problem to finding a set of the gain matrices, which would guarantee the stabilization. In this paper, we apply this method to a system of Van der Pol oscillators coupled in a cube-like configuration leading to O4-equivariance. We discuss group theoretic restrictions which help to shape our choice of control. Furthermore, we explicitly describe the domains in the parameter space for which the periodic solutions are stable.