Intermingled traveling waves in a ring of nonlocally coupled FitzHugh-Nagumo oscillators

¹ School of Science, Beijing University of Posts and Telecommunications - Beijing 100876, PRC

^(a) qldai@bupt.edu.cn
^(b) jzyang@bupt.edu.cn

Received: 3 April 2019
Accepted: 1 July 2019

Abstract

Nonlocally coupled systems may display fascinating dynamics such as chimera states. In this work, we report an intriguing pattern formation, intermingled traveling waves, in a ring of nonlocally coupled FitzHugh-Nagumo oscillators. For intermingled traveling waves with even number of traveling pulses, oscillators are spontaneously partitioned into two groups and each of them supports its own traveling pulses. Oscillators from different groups may be well mixed for random initial conditions. Adjacent oscillators perform the periodic oscillation with the same frequency and they may be in antiphase if belonging to different groups. For intermingled traveling waves with odd number of traveling pulses, possible antiphase between adjacent oscillators renders the state to possess character of Möbius strip. The stabilities of intermingled traveling waves are numerically investigated and the stability diagrams in different parameter planes are presented.