P092 Reversal of Wave Direction in Unidirectionally Coupled Oscillator Chains
Richard Gast*1, Guy Elisha2, Sara A. Solla3,4 , Neelesh A. Patankar5
1Department of Neuroscience, The Scripps Research Institute, San Diego, US
2Brain Mind Institute, EPFL, Lausanne, Switzerland
3Department of Neuroscience, Northwestern University, Evanston, US
4Department of Physics and Astronomy, Northwestern University, Evanston, US
5Department of Mechanical Engineering, Northwestern University, Evanston, US
*Email: rgast@scripps.edu
Introduction:Chains of coupled oscillators have been used to model animal behavior such as crawling, swimming, and peristalsis [1]. In such chains, phase lags between adjacent oscillators yield a propagating wave, which can either be anterograde (from proximal to distal) or retrograde (from distal to proximal). Switches in the direction of wave propagation have been related to increased flexibility, but also to pathology in biological systems. In Drosophila larvae, for example, switches in wave propagation are required for crawling, which has been achieved in a coupled oscillator chain model by applying an extrinsic input to distinct ends of the chain [2].
Methods:In this work, we explore a different, novel mechanism for reversing the wave propagation direction in a chain of unidirectionally coupled limit cycle oscillators. Instead of requiring tuned coupling or precisely timed local inputs, changes in the global extrinsic drive to the chain of oscillators suffices to control the direction of wave propagation. To this end, we consider a chain of unidirectionally coupled Wilson-Cowan (WC) oscillators [3]. The system is driven bySEandSI, which are extrinsic inputs globally applied to all excitatory and inhibitory populations in the chain, respectively.
Results:Combining numerical simulations and bifurcation analysis, we show that waves can propagate in anterograde or retrograde directions in the unidirectional chain of WC oscillators, despite uniform coupling and extrinsic input strengths across the chain [4]. We find that the direction of propagation is controlled by a disparity between the intrinsic frequency of the proximal oscillator and that of the more distal oscillators in the chain (see figures in [4]). The transition between these two behaviors finds explanation in the proximity of the chain's operational regime to a homoclinic bifurcation point, where small changes in the input translate to strong shifts in the oscillation period.
Discussion:Lastly, we discuss wave propagation in the context of phase oscillator networks. We describe a direct relationship between the intrinsic frequency differences between the proximal and distal chain elements, and the phase shift parameter of a phase coupling function [4]. This way, we analytically extend our numerical results to a more general phase oscillator model. Our work emphasizes the functional role that the existence of a homoclinic bifurcation plays for activity propagation in neural systems. The ability of this mechanism to operate on time scales as fast as the neural activity itself suggests that it could dynamically emerge in a variety of biological systems.
Acknowledgements
This work was funded by the by the National Institutes of Health (NIDDK Grant
No. DK079902 and No. DK117824), and National Science Foundation (OAC Grant No. 1931372).
References
[1] Kopell, N., & Ermentrout, G. B. (2003).The Handbook of Brain Theory and Neural Networks.
[2] Gjorgjieva, J., Berni, J., Evers, J. F., & Eglen, S. J. (2013).Frontiers in Computational Neuroscience, 7, 24.
[3] Wilson, H. R., & Cowan, J. D. (1972).Biophysical journal, 12(1), 1-24.
[4] Elisha, G., Gast, R., Halder, S., Solla, S. A., Kahrilas, P. J., Pandolfino, J. E., & Patankar, N. A. (2025).Physical Review Letters, 134(5), 058401.
