Canard cascading in networks with adaptive mean-field coupling

Balzer, J.; Berner, R.; Lüdge, K.; Wieczorek, Sebastian; Kurths, J.; Yanchuk, Serhiy

Canard cascading in networks with adaptive mean-field coupling

Files

PRL.pdf(9.92 MB)

Accepted Version

Date

2024-12-02

Authors

Balzer, J.

Berner, R.

Lüdge, K.

Wieczorek, Sebastian

Kurths, J.

Yanchuk, Serhiy

Publisher

American Physical Society

Published Version

10.1103/physrevlett.133.237401

Abstract

Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a slow-fast phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasistationary states. In this Letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. First, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Second, we uncover multiple saddle slow manifolds (unstable quasistationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organizes different unstable quasistationary states into an intricate slow-fast limit cycle. Although individual quasistationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes.

Keywords

Heteroclinic canard orbit , Canard cascading (CC)

Citation

Balzer, J., Berner, R., Lüdge, K., Wieczorek, S., Kurths, J. and Yanchuk, S. (2024) 'Canard cascading in networks with adaptive mean-field coupling', Physical Review Letters, 133(23), 237401 (7pp). https://doi.org/10.1103/physrevlett.133.237401