The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n = 1 ar...

A Liapunov type stability theory for high order systems of differential equations is developed. This is done by reduction to the classical case, using the theory of polynomial models.

The objective of this paper is to discuss the existence, bifurcation, and regularity, with respect to time and parameters, of bounded solutions of infinite dimensional equations. As an application of our results, we study homoclinic solutions of a nonlinear equation. Chow et al. [2, 31, using the Liapunov-Schmidt method, studied periodic and homoclinic solutions of j; + g(x) = -1f + pf(t), wher...

In this paper, we use the method of characteristics to study singularities in the flow of a parameterized family of extremals for an optimal control problem. By means of the Lyapunov–Schmidt reduction a characterization of fold and cusp points is given. Examples illustrate the local behaviors of the flow near these singular points. Singularities of fold type correspond to the typical conjugate ...

It is well known that solutions to the conformal formulation of the Einstein constraint equations are unique in the event that the mean curvature is constant (CMC) or near constant (near-CMC). However, the new far-from-constant mean curvature (farfrom-CMC) solution constructions due to Holst, Nagy, and Tsogtgerel and to Maxwell in 2009, and to Gicquad and collaborators in 2010, are based on deg...

A coupling inertial navigation sensor (INS) system may proven to be beneficial for performance improvement, especially when the manufacturing yield is very low for meeting the specification requirement of various applications. For instance, navigation grade sensors using the current fabrication process would yield one in every few hundreds which would meet the specification requirement after ca...

We introduce an algorithm for nonlinear noise reduction which is based on locally linear ts to the nonlinear dynamics. We claim that it is both robust and exible enough to apply it to a variety of experimental time series. In the second part of the paper we show its performance on data set A. The correlation dimension, Liapunov exponent and the Poincar e map are computed before and after the no...

Abstract A reaction–diffusion model, known as the Sel’kov–Schnakenberg is considered. The nonlinear stability of constant steady state studied by using a special Liapunov functional and maximum principle for regular solutions.