3 citations · 4 across the 5 of their papers we have counts for
6 papers
Heteroclinic connections between finite-amplitude periodic orbits emerging from a codimension two singularity
Thomas J. Bridges, David J. B. Lloyd, Daniel J. Ratliff +1
Heteroclinic connections between two distinct hyperbolic periodic orbits in conservative systems are important in a wide range of applications. On the other hand, it is theoretical…
Dynamic interactions and equilibrium configurations of pulses in the two-dimensional complex quintic Ginzburg-Landau equation
M R Turner, D J B Lloyd
This paper constructs a fast and effective novel numerical scheme which accurately calculates the dynamics of weakly-interacting pulses in the two-dimensional quintic-complex Ginzb…
Global bifurcation of localised 2D patterns emerging from spatial heterogeneity
Dan J. Hill, David J. B. Lloyd, Matthew R. Turner
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations contai…
Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation
David Lloyd, Ryan Goh, Jens D. M. Rademacher
We discuss some aspects of numerical continuation and bifurcation for partial differential equations, specifically pattern formation and coherent structures. For the sake of clarit…
Localized Patterns
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-under…
Radial amplitude equations for fully localised planar patterns
Dan J. Hill, David J. B. Lloyd
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, th…