Chimera states through invariant manifold theory. (29th June 2021)

• Record Type: Journal Article
• Authors: Eldering, Jaap; Lamb, Jeroen S W; Pereira, Tiago; Roque dos Santos, Edmilson
• Is Part Of: Nonlinearity. Volume 34:Number 8(2021)
• Page Start: 5344
• Page End: 5374
• Publication Date: 2021-06-29
• Subjects: chimera states -- complex networks -- normal hyperbolicity -- bifurcations; 37D10 -- 70K50 -- 34C29; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac0613
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We establish the existence of chimera states, simultaneously supporting synchronous and asynchronous dynamics, in a network of two symmetrically linked star subnetworks of identical oscillators with shear and Kuramoto–Sakaguchi coupling. We show that the chimera states may be metastable or asymptotically stable. If the intra-star coupling strength is of order ɛ, the chimera states persist on time scales at least of order 1/ ɛ in general, and on time-scales at least of order 1/ ɛ 2 if the intra-star coupling is of Kuramoto–Sakaguchi type. If the intra-star coupling configuration is sparse, the chimeras are asymptotically stable. The analysis relies on a combination of dimensional reduction using a Möbius symmetry group and techniques from averaging theory and normal hyperbolicity.