In 1979 Rosenblat developed a spectral method for studying bifurcation and stability problems. Drawing on an example from ordinary diierential equations, he showed quite elegantly that, although the method bore striking similarities with the Lyapunov-Schmidt procedure, the range of validity of his method was signiicantly greater. In the early '80s Rosenblat, Homsy and Davis developed these pion...

This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their ‘beliefs’ in each period in a boundedly rational way, according to a ‘fitness measure’ such as past realized profits. Price fluctuations are thus driven by an evolutionary dynami...

In this paper we describe a bifurcation analysis procedure for data driven background prediction under the conditions of a blinded signal box. The procedure uses the application of inverse cuts to properly measure the veto power of the different sets of cuts while not opening the signal box. This technique was first developed for a single background source in the stopped K experiments E787 and ...

*Correspondence: [email protected] 1Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P.R. China Full list of author information is available at the end of the article Abstract This paper is devoted to study a center problem and a weak center problem for cubic systems in Z4-equivariant vector fields. By computing the Lyapunov constants and periodic constants ca...

The divergence criterion has been shown to be helpful in distinguishing between suband supercritical Hopf bifurcations but its applicability is limited to systems whose divergence is sign definite. A step by step computational procedure which allows one to extend the applicability of the divergence criterion is derived by altering the system to an equivalent one with sign definite divergence. T...

This paper is concerned with the study of third order quadratic and autonomous systems and the interest is oriented to the stable periodic oscillations. From the “jerk” equation model, the classes of minimal complexity presenting a Hopf bifurcation are derived and their local characterization is carried out by means of a suitable harmonic balance technique. Other possible system reductions pres...

We consider a difference equation involving three parameters and a piecewise constant control function with an additional positive threshold λ. Treating the threshold as a bifurcation parameter that varies between 0 and∞, we work out a complete asymptotic and bifurcation analysis. Among other things, we show that all solutions either tend to a limit 1-cycle or to a limit 2-cycle and, we find th...

We consider positive solutions of the Dirichlet problem u′′(x) + λf(u(x)) = 0 in (−1, 1), u(−1) = u(1) = 0. depending on a positive parameter λ. We use two formulas derived in [18] to compute all solutions u where a turn may occur and to compute the direction of the turn. As an application, we consider quintic a polynomial f(u) with positive and distinct roots. For such quintic polynomials we c...

where D is a bounded domain with smooth boundary, g changes sign on D, and f is some function of class C1 such that f(0)= 0= f(1). Fleming’s results suggested that nontrivial steady-state solutions were bifurcating the trivial solutions u ≡ 0 and u ≡ 1. In order to investigate these bifurcation phenomena, it was necessary to understand the eigenvalues and eigenfunctions of the corresponding lin...

We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter space, reflecting the possibility of quasiconformal deformations. On the other hand, there is a natural bifurcation measure, supported on the closure of rigid p...