TY  - JOUR
A1  - Goldobin, Denis S.
A1  - Pikovskij, Arkadij
T1  - Effects of delayed feedback on Kuramoto transition
N2  - We develop a weakly nonlinear theory of the Kuramoto transition in an ensemble of globally coupled oscillators in presence of additional time-delayed coupling terms. We show that a linear delayed feedback not only controls the transition point, but effectively changes the nonlinear terms near the transition. A purely nonlinear delayed coupling does not effect the transition point, but can reduce or enhance the amplitude of collective oscillations
Y1  - 2006
UR  - http://www2.yukawa.kyoto-u.ac.jp/~ptpwww/link-supplement.html
U6  - https://doi.org/10.1143/PTPS.161.43
SN  - 0375-9687
ER  - 
TY  - JOUR
A1  - Goldobin, Denis S.
A1  - Pikovskij, Arkadij
T1  - Antireliability of noise-driven neurons
N2  - We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map
Y1  - 2006
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.73.061906
SN  - 1539-3755
ER  - 
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  - BOOK
A1  - Freude, Ulrike
A1  - Kuznetsov, Sergey P.
A1  - Pikovskij, Arkadij
T1  - Strange nonchaotic attractors : dynamics between order and chaos in Quasiperiodically Forced Systems
Y1  - 2006
SN  - 981-256633-3
PB  - World Scientific
CY  - Singapore
ER  -