ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


oscillations

Multistability in dynamical small world networks

  We explore phase multistability which takes place in an ensemble of periodic oscillators under the action of long-distance couplings, which appear randomly between the arbitrary cells. The  system under study is Kuromoto’s model with additional dynamical interconnections between phase oscillators. The sequence of bifurcations, which accompany increasing of the strength of the global coupling is determined. Regions of multistability existance are defined.

Phenomenon of the van der pol equation

  This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters. • The biography of van der Pol, history of his equation and supposed precursors. • The contribution of A.A. Andronov in the theory of self­oscillations.

Largest Lyapunov exponent of chaotic oscillatory regimes computing from point processes in the noise presence

We propose a modified method for computing of the largest Lyapunov exponent of chaotic oscillatory regimes from point processes at the presence of measurement noise that does not influence on the system’s dynamics. This modification allow a verification to be made of the estimated dynamical characteristics precision. Using the Rossler system in the regime of a phase-coherent chaos we consider features of application of this method to point processes of the integrate-and-fire and the threshold-crossing models. Download full version