TY - JOUR A1 - Schwabedal, Justus T. C. A1 - Pikovskij, Arkadij T1 - Effective phase description of noise-perturbed and noise-induced oscillations N2 - An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations. Y1 - 2010 U6 - https://doi.org/10.1140/epjst/e2010-01271-6 SN - 1951-6355 ER - TY - JOUR A1 - Schwabedal, Justus T. C. A1 - Pikovskij, Arkadij T1 - Effective phase dynamics of noise-induced oscillations in excitable systems N2 - We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations. Y1 - 2010 UR - http://link.aps.org/doi/10.1103/PhysRevE.81.046218 U6 - https://doi.org/10.1103/Physreve.81.046218 SN - 1539-3755 ER - TY - JOUR A1 - Schwabedal, Justus T. C. A1 - Pikovskij, Arkadij T1 - Phase description of stochastic oscillations JF - Physical review letters N2 - 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 state space, having a constant mean first return time. The approach allows us to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine isophases of observed irregular oscillations, providing a basis for a refined phase description in data analysis. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevLett.110.204102 SN - 0031-9007 VL - 110 IS - 20 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Schwabedal, Justus T. C. A1 - Pikovskij, Arkadij A1 - Kralemann, Björn A1 - Rosenblum, Michael T1 - Optimal phase description of chaotic oscillators JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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 the optimal isophases as Poincare surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rossler and Lorenz systems. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.026216 SN - 1539-3755 VL - 85 IS - 2 PB - American Physical Society CY - College Park ER -