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.

This paper describes the development of an efficient mechanical oscillator. It is capable of combining the energetic advantages of ballistic movement with cycle adjustability and active orbital control. Pneumatic artificial McKibben muscles are used as variable springs, from which the stiffness is varied in order to induce a limit cycle.

The well-known Hilbert’s 16th problem has remained unsolved since Hilbert proposed the 23 mathematical problems at the Second International Congress of Mathematics in 1900 [Hilbert, 1902]. Recently, a modern version of the second part of the 16th problem was formulated by Smale [1998], chosen as one of the 18 challenging mathematical problems for the 21st century. To be more specific, consider ...

The second part of Hilbert’s sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert’s sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equa...

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Suppose a group G is relatively hyperbolic with respect to a collection P of its subgroups and also acts properly, cocompactly on a CAT (0) (or δ–hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G,P). The CAT (0) structure provides a different boundary at infinity ∂X. In this article, we examine the connection between these two spaces at infinity. In parti...