We show that a one-sector real business cycle model with mild increasing returns-to-scale, variable capital utilization and saddle-path stability is able to produce qualitatively realistic business cycles driven solely by disturbances to government purchases. Due to an endogenous increase in labor productivity, a positive spending shock can lead to simultaneous increases in output, consumption,...

In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously computing high order parametrizations of the local stable and unstable manifolds. If the local manifolds intersect, the NewtonKantorovich theorem is applied to validate the existence of a so-cal...

In this paper we present an endogenous growth model with productive public capital and pollution. As to pollution we assume that it is a by-product of aggregate production and that it negatively affects utility of the household but not production possibilities directly. The paper studies the dynamics of the model and demonstrates that there exists either a unique balanced growth path which is a...

We consider the problem of convergence to a saddle point concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz, and Uzawa, such dynamics have been extensively used in diverse areas; there are, however, features that render their analysis nontrivial. These include lack guarantees when considered does not satisfy additional strictness properties also nonsmoothnes...

We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state correspond...

We introduce and solve a generalized 1+1D Lorentzian gravity model in which a certain subclass of baby-universes is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle pointand path integral techniques we show that for β < 1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The ...

Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path integral, but taking into account the h̄ dependence of both the amplitude and the phase of the intial wave function, thus giving rise to the need for complex clas...

OBJECTIVE To investigate the possible influences of saddle type on the incidence of "lower back pain" in a cross section of equestrian riders. METHODS 108 equestrian riders completed a questionnaire concerning their riding habits and whether they suffered from lower back pain. In particular they were asked whether they used a traditional style/general purpose saddle (GP) or a deep seated/West...

The stability of magnetic states and the mechanism for magnetic transitions can be analyzed in terms of the shape of the energy surface, which gives the energy as a function of the angles determining the orientation of the magnetic moments. Minima on the energy surface correspond to stable or metastable magnetic states and can represent parallel, antiparallel or, more generally, non-collinear a...

Many power engineering systems have dynamic state variables which can encounter constraints or limits affecting system stability. Voltage collapse is an instability associated with the occurrence of a saddle node bifurcation in the equations which model the electric power system. We investigate the effect of constraints on voltage collapse by studying the effect of constraining state variables ...