We introduce the concept of saddle points portfolio and we establish a connection between this concept and the approximate minima.

The task of finding saddle points on potential energy surfaces plays a crucial role in understanding the dynamics of a micromolecule as well as in studying the folding pathways of macromolecules like proteins. The problem of finding the saddle points on a high dimensional potential energy surface is transformed into the problem of finding decomposition points of its corresponding nonlinear dyna...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for communicating with chaotically behaving signal generators. The success of this type of nonlinear digital communication scheme relies on partitioning the phase space properly so that a good symbolic dynamics can be defined. A central problem is then how to encode an arbitrary message...

The uniform asymptotic description of electromagnetic pulse propagation in a single-resonance Lorentz medium is presented. The modern asymptotic theory used here relies on Olver's saddle-point method [Stud. Appl. Math. Rev. 12, 228 (1970)] together with the uniform asymptotic theory of Handelsman and Bleistein [Arch. Ration. Mech. Anal. 35, 267 (1969)] when two saddle points are at infinity (fo...

Saddle-node bifurcation occurs in a boost converter when parasitic inductor resistance is modeled. Closed-form critical conditions of the bifurcation are derived. If the parasitic inductor resistance is modeled, the saddle-node bifurcation occurs in the voltage mode control or in the current mode control with the voltage loop closed, but not in the current mode control with the voltage loop ope...

A method is presented for finding the ridge between first order saddle points on a multidimensional surface. For atomic scale systems, such saddle points on the energy surface correspond to atomic rearrangement mechanisms. Information about the ridge can be used to test the validity of the harmonic approximation to transition state theory, in particular to verify that second order saddle points...