All Outputs (3)

Oscillatory networks: insights from piecewise-linear modelling (2024)
Journal Article
Coombes, S., Şayli, M., Thul, R., Nicks, R., Porter, M. A., & Lai, Y. M. (2024). Oscillatory networks: insights from piecewise-linear modelling. SIAM Review, 66(4), 619-679. https://doi.org/10.1137/22M1534365

There is enormous interest-both mathematically and in diverse applications-in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is... Read More about Oscillatory networks: insights from piecewise-linear modelling.

Phase and amplitude responses for delay equations using harmonic balance (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Phase and amplitude responses for delay equations using harmonic balance. Physical Review E, 110(1), Article L012202. https://doi.org/10.1103/PhysRevE.110.L012202

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a gr... Read More about Phase and amplitude responses for delay equations using harmonic balance.

Insights into oscillator network dynamics using a phase-isostable framework (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Insights into oscillator network dynamics using a phase-isostable framework. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1), Article 013141. https://doi.org/10.1063/5.0179430

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolu... Read More about Insights into oscillator network dynamics using a phase-isostable framework.