The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

This paper develops a Chebyshev–Taylor spectral method for studying stable/unstable
manifolds attached to periodic solutions of differential equations. The work exploits the …

It has long been known that non-steady state and periodic catalytic reactor operation in
terms of temperature, pressure, and composition can lead to higher overall productivity …

We present an efficient numerical method for computing Fourier--Taylor expansions of (un)
stable manifolds associated with hyperbolic periodic orbits. Three features of the method are …

We present a numerical method for finding and continuing heteroclinic connections of vector
fields that involve periodic orbits. Specifically, we concentrate on the case of a codimension …

We study the effects of a non-specified infectious disease of the predator on the dynamics a
predator–prey system, by evaluating the dynamics of a three-dimensional model. The …

Isochrons are foliations of phase space that extend the notion of phase of a stable periodic
orbit to the basin of attraction of this periodic orbit. Each point in the basin of attraction lies on …

Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of
study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos …

This paper considers two point boundary value problems for conservative systems defined
in multiple coordinate systems, and develops a flexible a posteriori framework for computer …

We study grain boundaries between striped phases in the prototypical Swift--Hohenberg
equation. We propose an analytical and numerical far-field-core decomposition that allows …