74 citations · 169 across the 11 of their papers we have counts for
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Dead zones and phase reduction of coupled oscillators
Peter Ashwin, Christian Bick, Camille Poignard
A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in…
Excitable Networks for Finite State Computation with Continuous Time Recurrent Neural Networks
Peter Ashwin, Claire M Postlethwaite
Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computa…
Weak tracking in nonautonomous chaotic systems
Hassan Alkhayuon, Peter Ashwin
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to "parameter shifts" between two asymptotically steady values of a sy…
The Echo Index and multistability in input-driven recurrent neural networks
Andrea Ceni, Peter Ashwin, Lorenzo Livi +1
A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it ``forgets'' any internal states of the driven (nonautonomous) system and…
State-dependent effective interactions in oscillator networks through coupling functions with dead zones
Peter Ashwin, Christian Bick, Camille Poignard
The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling func…
Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems
Karl Nyman, Peter Ashwin, Peter Ditlevsen
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We class…