329 citations · 493 across the 15 of their papers we have counts for
15 papers
A parsimonious model of blood glucose homeostasis
Eric Ng, Jaycee Morgan Kaufman, Lennaert van Veen +1
The mathematical modelling of biological systems has historically followed one of two approaches: comprehensive and minimal. In comprehensive models, the involved biological pathwa…
Transitions in large eddy simulation of box turbulence
Lennaert van Veen, Genta Kawahara, Tatsuya Yasuda
One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approxima…
Hidden symmetry in a Kuramoto-Sivashinsky initial-boundary value problem
Pietro-Luciano Buono, Lennaert van Veen, Eryn Frawley
We investigate the bifurcation structure of the Kuramoto-Sivashinsky equation with homogeneous Dirichlet boundary conditions. Using hidden symmetry principles, based on an extended…
Sub critical transition to turbulence in three-dimensional Kolmogorov flow
Lennaert van Veen, Susumu Goto
We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the l…
Green's function-based time stepping for the Kuramoto-Sivashinsky initial-boundary value problem
Lennaert van Veen
Both theoretical and numerical studies of the Kuramoto-Sivashinsky equation have mostly considered periodic boundary conditions. In this setting, the Fourier decomposition of the s…
Periodic solutions to a mean-field model for electrocortical activity
Lennaert van Veen, Kevin Green
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitor…
PAMPAC: A Parallel Adaptive Method for Pseudo-Arclength Continuation
Dhavide Aruliah, Lennaert van Veen, Alex Dubitski
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an…
Open-source tools for dynamical analysis of Liley's mean-field cortex model
Kevin R. Green, Lennaert van Veen
Mean-field models of the mammalian cortex treat this part of the brain as a two-dimensional excitable medium. The electrical potentials, generated by the excitatory and inhibitory…
The Significance of Simple Invariant Solutions in Turbulent Flows
Genta Kawahara, Markus Uhlmann, Lennaert van Veen
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances i…
A homoclinic tangle on the edge of shear turbulence
Lennaert van Veen, Genta Kawahara
Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate b…
Metabifurcation analysis of a mean field model of the cortex
Federico Frascoli, Lennaert van Veen, Ingo Bojak +1
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions i…
On matrix-free computation of 2D unstable manifolds
Lennaert van Veen, Genta Kawahara, Matsumura Atsushi
Recently, a flexible and stable algorithm was introduced for the computation of 2D unstable manifolds of periodic solutions to systems of ordinary differential equations. The main…
An integrating factor matrix method to find first integrals
K. V. I. Saputra, G. R. W. Quispel, L. van Veen
In this paper we developed an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along…
The saddle-node-transcritical bifurcation in a population model with constant rate harvesting
K. V. I. Saputra, L. van Veen, G. R. W. Quispel
We study the interaction of saddle-node and transcritical bifurcations in a Lotka-Volterra model with a constant term representing harvesting or migration. Because some of the equi…
The dynamics of a low-order coupled ocean-atmosphere model
L. van Veen, F. Verhulst, T. Opsteegh
A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is stu…