– We demonstrate synchronization transition in a large ensemble of non-identical chaotic oscillators, globally coupled via the mean field. We show that this coherent behaviour is due to synchronization of phases of these oscillators, while their amplitudes remain chaotic. Two types of transition, depending on the phase coherence properties of the individual systems, are described. A number of p...

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order ao2 is dissipation. In systems with many spacially couple...

We model networks of identical, all-to-all pulse-coupled phase oscillators with white noise, in the limit of infinite network size and Dirac pulses, using a Fokker-Planck equation for the phase probability density. We give analytical, constructive existence and uniqueness results for stationary states (i.e. timeindependent densities), and derive and study a one-dimensional eigenvalue equation f...

In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbatio...

This paper provides contributions to the study of phase synchronization transient two identical linear LC oscillators, coupled through a resistor. The main contribution is obtaining an exact equation that represents, as function time, evolution angle between from initial condition until synchronization. It demonstrated system has equilibrium points, one unstable when equal π, and other stable i...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...