TY - JOUR A1 - Zheng, Chunming A1 - Toenjes, Ralf A1 - Pikovskij, Arkadij T1 - Transition to synchrony in a three-dimensional swarming model with helical trajectories JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevE.104.014216 SN - 2470-0045 SN - 2470-0053 VL - 104 IS - 1 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Zheng, Chunming A1 - Pikovskij, Arkadij T1 - Stochastic bursting in unidirectionally delay-coupled noisy excitable systems JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We show that "stochastic bursting" is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by an idealized coupled point processwith a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, the pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in good agreement with the simulations with a network of theta-neurons. Published under license by AIP Publishing. Y1 - 2019 U6 - https://doi.org/10.1063/1.5093180 SN - 1054-1500 SN - 1089-7682 VL - 29 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Gong, Chen Chris A1 - Zheng, Chunming A1 - Toenjes, Ralf A1 - Pikovskij, Arkadij T1 - Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, the formation of stable multicluster states has been observed in this regime. However, we argue here that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. By monitoring the induced change in certain integrals of motion, we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function as well as additional amplitude dynamics, multiclusters can occur naturally. Published under license by AIP Publishing. Y1 - 2019 U6 - https://doi.org/10.1063/1.5084144 SN - 1054-1500 SN - 1089-7682 VL - 29 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Zheng, Chunming A1 - Pikovskij, Arkadij T1 - Delay-induced stochastic bursting in excitable noisy systems JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We show that a combined action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic timescales in the problem are well separated, is used to describe statistical properties such as the power spectral density and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate, and the probability to induce a spike during the delay action can be calculated from the solutions of a stationary and a forced Fokker-Planck equation. Y1 - 2018 U6 - https://doi.org/10.1103/PhysRevE.98.042148 SN - 2470-0045 SN - 2470-0053 VL - 98 IS - 4 PB - American Physical Society CY - College Park ER -