The well-known Van der Pol equation with delayed feedback is considered. It assumed that the delay factor large enough. In study of dynamics, critical cases in problem stability zero equilibrium state are identified. shown they have infinite dimension. For such cases, special local analysis methods been developed. main result construction nonlinear evolutionary boundary value problems, which pl...

Under four assumptions such that 1) Einstein’s theory of gravity is correct, 2) existence of foliation by geodesic slicing, 3) the trace of the extrinsic curvature, K, is negative at the present time in observed region, that is, the observed universe is now expanding, 4) the strong energy condition is satisfied, we show that Hv0t0 ≤ 1, where Hv ≡ −K/3 agrees with the Hubble parameter in the cas...

The van der Pol oscillator is the prototypical self-sustained oscillator and has been used to model nonlinear behavior in biological and other classical processes. We investigate how quantum fluctuations affect phase locking of one or many van der Pol oscillators. We find that phase locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments ...

We explore the transition to in-phase synchronization in globally coupled oscillator arrays, and compare results for van der Pol arrays with Josephson junction arrays. Our approach yields in each case an analytically tractable iterative map; the resulting stability formulas are simple because the expansion procedure identifies natural parameter groups. A third example, an array of Duffing-van d...

In the article, existence of solutions for Van der Pol differential equation is proved, and approximate structure such in analyticity domain obtained. proof, majorant method was applied not to right side equation, as per usual, but solution nonlinear under consideration. Results numerical study are presented.

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the mo...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

In the last three quarters of the fifteenth century Spain, like the rest of Europe, was under the spell of Flemish art. The realism of the north had a strong appeal to Spanish taste, and the technical discoveries of Flemish painting and the new iconographies from Flanders and Germany were enthusiastically received. In the second half of the century in particular, tapestries, paintings, and scul...