We have fabricated NbSe3 structures with widths comparable to the Fukuyama-Lee-Rice phase-coherence length. For samples already in the two-dimensional pinning limit, we observe a crossover from twodimensional to one-dimensional collective pinning when the crystal width is less than 1.6 mm, corresponding to the phase-coherence length in this direction. Our results show that surface pinning is ne...

This paper treats limit cycles caused by friction. The goal has been to explain phenomena that have been observed experimentally in mechatronic systems. Experiments have shown that oscillations of qualitatively different types can be obtained simply by changing controller specifications. Stiction is important in some cases but not in others. Necessary conditions for limit cycle are given for th...

Dispersion curves to a oscillatory reaction-diffusion system with the selfconsistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point of inflection which separates the dispersion curves into two branches corresponding to trigger and phase waves, moves according to the value of the advection...

In this paper we classify the phase portraits in the Poincaré disc of the centers of the generalized class of Kukles systems ẋ = −y, ẏ = x+ axy + bxy, symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential s...

We consider the class of polynomial differential equations ẋ = λx + Pn(x, y), ẏ = μy + Qn(x, y) in R where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= μ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non–e...

In this paper, we show that perturbing a simple 3-d quadratic system with a center-type singular point can yield at least 10 small-amplitude limit cycles around a singular point. This result improves the 7 limit cycles obtained recently in a simple 3-d quadratic system around a Hopf singular point. Compared with Bautin’s result for quadratic planar vector fields, which can only have 3 small-amp...

We investigate the dynamics of two-strategy replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T . We analyze two models: in the first, all terms in the fitness are delayed, while in the second, only oppositestrategy terms are delayed. We compare the two models via a linear homotopy. Taking the delay T as a bifurcati...

We examine whether price dispersion is an equilibrium phenomenon or a cyclical phenomenon. We develop a finite strategy model of price dispersion based on the infinite strategy model of Burdett and Judd (1983). Adopting an evolutionary standpoint, we examine the stability of dispersed price equilibrium under perturbed best response dynamics. We conclude that when both sellers and consumers part...

In this paper we study the number of limit cycles bifurcating from isochronous surfaces of revolution contained in R, when we consider polynomial perturbations of arbitrary degree. The method for studying these limit cycles is based in the averaging theory and in the properties of Chebyshev systems. We present a new result on averaging theory and generalitzations of some classical Chebyshev sys...

We study the limit cycles of a generalized Kukles polynomial differential systems using the averaging theory of first and second order.