4 citations · 23 across the 17 of their papers we have counts for
10 papers · 1 filter
A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Lucía 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…
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…
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…
A symmetry property for elliptic equations on the sphere
Phillipo Lappicy
The goal of this paper is to study how the symmetry of the spherical domain influences solutions of elliptic equations on such domain. The method pursued is a variant of the moving…
Ginzburg-Landau patterns in circular and spherical geometries: vortices, spirals and attractors
Jia-Yuan Dai, Phillipo Lappicy
This paper consists of three results on pattern formation of Ginzburg-Landau -armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely…
Conley's index and connection matrices for non-experts
Phillipo Lappicy
This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the nec…
Unbounded Sturm attractors for quasilinear equations
Phillipo Lappicy, Juliana Fernandes Pimentel
We analyze the asymptotic dynamics of quasilinear parabolic equations when solutions may grow up (i.e., blow up in infinite time). For such models, there is a global attractor whic…
Sturm attractors for quasilinear parabolic equations
Phillipo Lappicy
The goal of this paper is to construct explicitly the global attractors of quasilinear parabolic equations, as it was done for the semilinear case by Brunovský and Fiedler (1986),…
Sturm attractors for quasilinear parabolic equations with singular coefficients
Phillipo Lappicy
The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the sing…
A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
Phillipo Lappicy, Bernold Fiedler
Lyapunov functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Zelenyak (1968) and Matano (1988) constructed a Lyapun…