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math.DS2024
Phase and amplitude responses for delay equations using harmonic balance
Rachel Nicks, Robert Allen, Stephen Coombes
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 d…
math.DS2023
Insights into oscillator network dynamics using a phase-isostable framework
Rachel Nicks, Robert Allen, Stephen Coombes
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled os…