Sergiy Yanchuk

TL;DR: One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic beta-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bIfurcations on one side of the arms and saddle-node bifutures on the other.

TL;DR: In this paper, the authors examined the problem of partial synchronization (or clustering) in diffusively coupled arrays of identical chaotic oscillators with periodic boundary conditions and proved the existence of partially synchronized states for systems of three and four oscillators.

TL;DR: In this paper, the authors considered the transverse stability of a pair of symmetrically coupled, identical Rossler systems and showed that desynchronization is associated with different orbits undergoing transverse pitchfork or period-doubling bifurcations.

TL;DR: It is shown that the synchronized state is shifted away from the symmetric manifold, and the magnitude of this shift is expressed in terms of the coupling strength and the mismatch parameter.

TL;DR: Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed, respectively, in terms of the subcritical, supercritical nature of the riddling biforcations.