32 citations · 52 across the 9 of their papers we have counts for
10 papers
Chaotic motion and singularity structures of front solutions in multi-component FitzHugh-Nagumo-type systems
Martina Chirilus-Bruckner, Peter van Heijster, Jens D. M. Rademacher
We study the dynamics of front solutions in a certain class of multi-component reaction-diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly cou…
Stability of asymptotic waves in the Fisher-Stefan equation
T. T. H. Bui, P. van Heijster, R. Marangell
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonl…
Random Evolutionary Dynamics in Predator-Prey Systems Yields Large, Clustered Ecosystems
Christian Hamster, Jorik Schaap, Peter van Heijster +1
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is class…
Waves in a Stochastic Cell Motility Model
Christian Hamster, Peter van Heijster
In Bhattacharya et al. (Science Advances, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied. Both at the microscopic level, where the…
Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system
Christopher Brown, Gianne Derks, Peter van Heijster +1
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a t…
Stability analysis of a modified Leslie-Gower predation model with weak Allee effect on the prey
Claudio Arancibia-Ibarra, José Flores, Peter van Heijster
In this manuscript, we study a Leslie-Gower predator-prey model with a hyperbolic functional response and weak Allee effect. The results reveal that the model supports coexistence…
Traveling wave solutions in a model for tumor invasion with the acid-mediation hypothesis
P. N. Davis, P. van Heijster, R. Marangell +1
In this manuscript, we prove the existence of slow and fast traveling wave solutions in the original Gatenby--Gawlinski model. We prove the existence of a slow traveling wave solut…
Absolute instabilities of travelling wave solutions in a Keller-Segel model
P. N. Davis, P. van Heijster, R. Marangell
We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, subl…
A geometric construction of travelling wave solutions to the Keller-Segel model
Kristen Harley, Peter van Heijster, Graeme Pettet
We study a version of the Keller-Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using…
Novel solutions for a model of wound healing angiogenesis
Kristen Harley, Peter van Heijster, Robert Marangell +2
We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In thi…