76 citations · 331 across the 11 of their papers we have counts for
6 papers · 1 filter
Qualitative and Quantitative Stability Analysis of Penta-rhythmic Circuits
Justus T. C. Schwabedal, Drake E. Knapper, A. L. Shilnikov
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a…
Key bifurcations of bursting polyrhythms in 3-cell central pattern generators
Jeremy Wojcik, Robert Clewley, Justus Schwabedal +1
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircui…
Phase Description of Stochastic Oscillations
Justus T. C. Schwabedal, Arkady Pikovsky
We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the s…
Optimal Phase Description of Chaotic Oscillators
Justus T. C. Schwabedal, Arkady Pikovsky, Björn Kralemann +1
We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define…
Effective phase description of noise-perturbed and noise-induced oscillations
Justus T. C. Schwabedal, Arkady Pikovsky
An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density…
Effective phase dynamics of noise-induced oscillations in excitable systems
Justus T. C. Schwabedal, Arkady Pikovsky
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribu…