TY - JOUR
T1 - Phase-locking in k-partite networks of delay-coupled oscillators
AU - Singha, Joydeep
AU - Ramaswamy, Ramakrishna
N1 - Funding Information:
We thank Nirmal Punetha for extensive discussions during the course of this work. RR is a recipient of the J. C. Bose National Fellowship of the Science and Engineering Research Board, India. JS acknowledges the support of Indian Institute of Technology Delhi, India, in the form of Institute Post Doctoral Fellowship (IPDF).
Funding Information:
We thank Nirmal Punetha for extensive discussions during the course of this work. RR is a recipient of the J. C. Bose National Fellowship of the Science and Engineering Research Board, India. JS acknowledges the support of Indian Institute of Technology Delhi, India, in the form of Institute Post Doctoral Fellowship (IPDF).
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2022/4/1
Y1 - 2022/4/1
N2 - We examine the dynamics of an ensemble of phase oscillators that are divided in k sets, with time-delayed coupling interactions only between oscillators in different sets or partitions. The network of interactions thus forms a k−partite graph. A variety of phase-locked states are observed; these include, in addition to the fully synchronized in-phase solution, splay cluster solutions in which all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are integer multiples of 2π/k. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions. With increase in time-delay, there is an increase in multistability, the generic solutions coexisting with a number of other partially synchronized solutions. The Ott-Antonsen ansatz is applied for the special case of a symmetric k−partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. Agreement with numerical results for the specific case of oscillators on a tripartite lattice (the k=3 case) is excellent.
AB - We examine the dynamics of an ensemble of phase oscillators that are divided in k sets, with time-delayed coupling interactions only between oscillators in different sets or partitions. The network of interactions thus forms a k−partite graph. A variety of phase-locked states are observed; these include, in addition to the fully synchronized in-phase solution, splay cluster solutions in which all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are integer multiples of 2π/k. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions. With increase in time-delay, there is an increase in multistability, the generic solutions coexisting with a number of other partially synchronized solutions. The Ott-Antonsen ansatz is applied for the special case of a symmetric k−partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. Agreement with numerical results for the specific case of oscillators on a tripartite lattice (the k=3 case) is excellent.
UR - http://www.scopus.com/inward/record.url?scp=85126039359&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2022.111947
DO - 10.1016/j.chaos.2022.111947
M3 - Article
AN - SCOPUS:85126039359
SN - 0960-0779
VL - 157
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 111947
ER -