6 papers
Global Continuation of Stable Periodic Orbits in Systems of Competing Predators
Kevin E. M. Church, Jia-Yuan Dai, Olivier Hénot +2
We develop a continuation technique to obtain global families of stable periodic orbits, delimited by transcritical bifurcations at both ends. To this end, we formulate a zero-find…
The Bianchi IX Attractor in Modified Gravity
Ester Beatriz, Everaldo Bonotto, Phillipo Lappicy
We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as HoÅava-Lifshitz, - or gravity), which are expected to descr…
A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
LucÃa Alonso Mozo, Olivier Hénot, Phillipo Lappicy
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to…
Oscillatory spacelike singularities: The Bianchi type vacuum models
Phillipo Lappicy, Claes Uggla
The Bianchi type , and vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic init…
On bifurcation from infinity: a compactification approach
José M. Arrieta, Juliana Fernandes, Phillipo Lappicy
We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically sublinear. As the parameter crosses critical…
Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria
Alejandro López-Nieto, Phillipo Lappicy, Nicola Vassena +2
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a…