The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown that the onset of a synchronous regime is based on the appearance of a phase relation between the interacting chaotic oscillator frequency components of Fourier spectra. The criterion of synchronization of spectral components as well as the measure of synchronization has been discussed. The universa...

In this study, nonlinear wave phenomena related to reections and transmissions of the phase-inversion-waves around the discontinuity of the system consisting of two parts of coupled van der Pol oscillators are investigated. Behavior of the phase-inversion-waves around a discontinuity in a coupled system consisting of two kinds of arrays of van der Pol oscillators classi ed into 8 types by compu...

We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series. 1. Preliminaries. In [8] the following odd looking integral evaluation is obtained. ∫ ∞ 0 ( 3− 2 √ 2 cos (t log 2) ) |ζ (1/2 + it)| t2 + 1/4 dt = π log 2. (1) This identity turns out—formally—to be a case of a ...

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent o...

A one dimensional phase model for the classic two dimensional van der Pol oscillator is developed. This model is restricted to the relaxed case, and its construction is based on the slow and fast transitions the phase goes through during its cycle. An application of the phase model is included in which synchronization of two coupled van der Pol oscillators is analyzed and even used to calculate...

In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...

Self-excited oscillation problem occurring from a triode electrical circuit has been modelled by van der Pol. Until now, the exact solution to Pol equation is not available. This paper focuses on finding new method for solving simply and accurately. There exists several approximate iterative methods available in literature equation, such as, successive approximation method. The simple, but inac...

We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear, multiparameter models is an apparently inherent insensitivity to large-magnitude variations in certain linear combinations of parameters. This phenomenon of "sloppine...

The work is devoted to the systematic research of the periodic, quasi-periodic or chaotic oscillations and the coexistence in the nonlinear Duffing-van der Pol type dynamical systems describing processes and phenomena in nature or engineering. The achieved result is the elaboration of the basic theory for searching nonlinear effects based on the concepts of periodic skeletons, bifurcation theor...