19 citations · 44 across the 7 of their papers we have counts for
9 papers
A theory for detecting the Turing instability on static and temporal multiplex networks
Joshua Ritchie
The purpose of this work is to introduce and discuss a general framework for performing a linear instability analysis on multiplex networks, in the absence of inter-layer diffusion…
Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields
Joshua Ritchie
The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar fiel…
A general formalism for coupling scalar fields to the Einstein equations without a variational principle
Joshua Ritchie
The purpose of this work is to discuss how matter fields are coupled to gravity within the framework of General Relativity. Our particular focus here is on the coupling of scalar f…
Turing instability and pattern formation on directed networks
Joshua Ritchie
Pattern formation, arising from systems of autonomous reaction-diffusion equations, on networks has become a common topic of study in the scientific literature. In this work we foc…
Bianchi I "asymptotically Kasner" solutions of the Einstein scalar field equations
Joshua Ritchie
In this work we investigate the asymptotic behaviour of solutions to the Einstein equations with a minimally coupled scalar field. The primary focus of the present paper here estab…
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…