15 citations · 16 across the 8 of their papers we have counts for
9 papers
Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
Maciej J. Capinski, Shane Kepley, Jason D. Mireles James
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…
Global analysis of regulatory network dynamics: equilibria and saddle-node bifurcations
Shane Kepley, Konstantin Mischaikow, Elena Queirolo
In this paper we describe a combined combinatorial/numerical approach to studying equilibria and bifurcations in network models arising in Systems Biology. ODE models of the dynami…
Extending combinatorial regulatory network modeling to include activity control and decay modulation
Bree Cummins, Marcio Gameiro, Tomas Gedeon +3
Understanding how the structure of within-system interactions affects the dynamics of the system is important in many areas of science. We extend a network dynamics modeling platfo…
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…