147 citations · 1.1k across the 23 of their papers we have counts for
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cond-mat.dis-nn2002★ 54 cited
Unstable attractors induce perpetual synchronization and desynchronization
Marc Timme, Fred Wolf, Theo Geisel
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network…
cond-mat.dis-nn2002★ 147 cited
Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators
Marc Timme, Fred Wolf, Theo Geisel
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to…
cond-mat.dis-nn2002★ 125 cited
Prevalence of unstable attractors in networks of pulse-coupled oscillators
Marc Timme, Fred Wolf, Theo Geisel
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in net…