67 citations · 169 across the 13 of their papers we have counts for
16 papers
Turing and wave instabilities in hyperbolic reaction-diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation
Joshua Ritchie, Andrew L. Krause, Robert A. Van Gorder
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct featu…
Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged
Robert A. Van Gorder
We describe how to control the motion -- both speed and propagation direction -- of a nonlinear traveling wave in real time via soliton management with time-varying dispersion/diff…
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices
Robert A. Van Gorder, Andrew L. Krause, Boris A. Malomed +1
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-pha…
Turing conditions for pattern forming systems on evolving manifolds
Robert A. Van Gorder, Václav Klika, Andrew L. Krause
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in d…
Amplitude death criteria for coupled complex Ginzburg-Landau systems
Robert A. Van Gorder, Andrew L. Krause, James A. Kwiecinski
Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, an…
Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations
James A. Kwiecinski, Attila Kovacs, Andrew L. Krause +2
The discovery of Pluto's small moons in the last decade brought attention to the dynamics of the dwarf planet's satellites. With such systems in mind, we study a planar -body sy…
Chaos in a non-autonomous nonlinear system describing asymmetric water wheels
Ashish Bhatt, Robert A. Van Gorder
We use physical principles to derive a water wheel model under the assumption of an asymmetric water wheel for which the water inflow rate is in general unsteady (modeled by an arb…
Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
Robert A. Van Gorder, Andrew L. Krause, Ferran Brosa Planella +1
We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can…
Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media
Andrew L. Krause, Dmitry Beliaev, Robert A. Van Gorder +1
We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatiall…
Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold
Andrew L. Krause, Dmitry Beliaev, Robert A. Van Gorder +1
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of n…
Opinion formation and distribution in a bounded confidence model on various networks
X. Flora Meng, Robert A. Van Gorder, Mason A. Porter
In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a…
Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains
Armin Kekić, Robert A. Van Gorder
We study solitary wave propagation in 1D granular crystals with Hertz-like interaction potentials. We consider interfaces between media with different exponents in the interaction…
A Fractional Diffusion Equation for an n-Dimensional Correlated Levy Walk
J. P. Taylor-King, R. Klages, S. Fedotov +1
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across…
Reduction of dimension for nonlinear dynamical systems
Heather A. Harrington, Robert A. Van Gorder
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one…
Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation
Robert A. Van Gorder
The Hasimoto transformation between the classical LIA (local induction approximation, a model approximating the motion of a thin vortex filament) and the nonlinear Schrödinger equa…
Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices
Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger (DNLS) equations with the attrac…