6 papers
Rational design of complex phenotype via network models
Marcio Gameiro, Tomas Gedeon, Shane Kepley +1
We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this…
Computing linear extensions for polynomial posets subject to algebraic constraints
Shane Kepley, Konstantin Mischaikow, Lun Zhang
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements…
A constructive proof of the Cauchy-Kovalevskaya theorem for ordinary differential equations
Shane Kepley, Tianhao Zhang
We give a constructive proof of the classical Cauchy-Kovalevskaya theorem in the ODE setting which provides a sufficient condition for an initial value problem to have a unique ana…
Homoclinic dynamics in a restricted four body problem
Shane Kepley, J. D. Mireles James
We describe a method for computing an atlas for the stable or unstable manifold attached to an equilibrium point, and implement the method for the saddle-focus libration points of…
Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem
Shane Kepley, J. D. Mireles James
We prove the existence of chaotic motions in a planar restricted four body problem, establishing that the system is not integrable. The idea of the proof is to verify the hypothese…
Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds
William D. Kalies, Shane Kepley, J. D. Mireles James
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The proc…