We introduce a time-to-build technology in a Solow model with bounded technological progress. Our analysis shows that the system may be asymptotically stable, or it can produce stability switches and Hopf bifurcations when time delay varies. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Nume...

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n–manifold (n ≥ 7). This paper may be viewed as a generalization of Siebenmann’s famous collaring theorem to open manifolds with non-stable fundamental group syst...

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M, g), 3 ≤ n ≤ 7, can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embed...

In this article, we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work do not assume that convergence occurs an isolated attractor but instead allow a stable manifold. On the manifold target function is constant and oscillations of iterates in tangential direction may be significantly larger than ones normal direction....

This paper is concerned with the asymptotic behavior of solutions to an outflow problem for one-dimensional bipolar quantum Navier-Stokes-Poisson equations in half space. First, by means manifold theory and center theorem, we show existence spatial decay rate stationary solution provided boundary strength small enough. Next, based on elaborate energy estimates, prove that asymptotically stable ...

In this paper, a system of three globally coupled limit cycle oscillators with a linear time-delayed coupling are investigated. Considering the delay as a parameter, we also study the effect of time delay on the dynamics. Next, Hopf bifurcations induced by time delays using the normal form theory and center manifold reduction are obtained. Based on the symmetric Hopf bifurcation theorem, we inv...

A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the ...