We show that in a canonical one-sector AK model of endogenous growth with a generalized cash-in-advance constraint, the growth and velocity effects of money are closely related to the local stability properties of the economy’s balanced growth paths. When a positive fraction (excluding 100 percent) of gross investment is subject to the liquidity constraint, the economy displays saddle-path stab...

We study the saddle-node bifurcation of a spatially homogeneous oscillation in a reactiondiffusion system posed on the real line. Beyond the stability of the primary homogeneous oscillations created in the bifurcation, we investigate existence and stability of wave trains with large wavelength that accompany the homogeneous oscillation. We find two different scenarios of possible bifurcation di...

This paper studies the solvability and stability of a generalized saddle-point system in finiteand infinite-dimensional spaces. Sharp solvability conditions and stability estimates are derived.

Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about nonperturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. Ho...

We investigate minimum energy paths of the quasi-linear problem with the p-Laplacian operator and a double-well potential. We adapt the String method of E., Ren, and Vanden-Eijnden (J. Chem. Phys., vol. 126 2007) to locate saddle-type solutions. In one-dimension, the String method is shown to find a minimum energy path that can align along one-dimensional “ridges” of saddle-continua. We then ap...

In this article, we present a bifurcation and stability analysis on the double-diffusive convection. The main objective is to study 1) the mechanism of the saddle-node bifurcation and hysteresis for the problem, 2) the formation, stability and transitions of the typical convection structures, and 3) the stability of solutions. It is proved in particular that there are two different types of tra...

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddl...

Here the path integral is over real metrics modulo coordinate transformations, G denotes a renormalized Newton constant and the · · · indicate higher derivative terms like R, etc. There may also be nonlocal terms related to the conformal anomaly [2]. The integral over μ produces the volume fixing delta function δ( ∫ dx √ g − V ). If this integral were done in the saddle point approximation, the...

Saddle point search on an energy surface has broad applications in fields like materials science, physics, chemistry, and biology. In this paper, we present the shrinking dimer dynamics (SDD), a dynamic system which can be applied to locate a transition state on an energy surface corresponding to an index-1 saddle point where the Hessian has a negative eigenvalue. By searching for the saddle po...