TITLE:
Time-Delay Effects on Synchronization of Coupled Slow-Fast Systems
AUTHORS:
Yuanguang Zheng, Jianjian Zeng
KEYWORDS:
Synchronization, Slow-Fast System, Time-Delay, Geometric Singular Perturbation Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.4,
April
20,
2021
ABSTRACT: Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.