106 citations · 398 across the 15 of their papers we have counts for
4 papers · 1 filter
Distinguishing between long-transient and asymptotic states in a biological aggregation model
Jonathan R. Potts, Kevin J. Painter
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion…
Weakly nonlinear analysis of a two-species non-local advection-diffusion system
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection…
Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent pa…
Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has be…