Chimera states through invariant manifold theory

Author(s)

Eldering, Jaap ^[1] ; Lamb, Jeroen S. W. ^[2] ; Pereira, Tiago ^{[1, 2]} ; dos Santos, Edmilson Roque ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Comp Sci, Sao Paulo - Brazil

^[2] Imperial Coll London, Dept Math, London SW7 2AZ - England

• Document type: Journal article
• Source: Nonlinearity; v. 34, n. 8, p. 5344-5374, AUG 2021.
• Web of Science Citations: 0

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 e, the chimera states persist on time scales at least of order 1/e in general, and on time-scales at least of order 1/e (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 Mobius symmetry group and techniques from averaging theory and normal hyperbolicity. (AU)

• FAPESP's process: 18/10349-4 - Reconstruction of complex networks from data
• Grantee: Edmilson Roque dos Santos
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 15/25947-6 - Stability and synchronization in power networks
• Grantee: Jacob Eldering
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC