29 citations · 73 across the 14 of their papers we have counts for
4 papers · 1 filter
Spatial Dynamics with Heterogeneity
Denis D. Patterson, Simon A. Levin, A. Carla Staver +1
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling g…
Probabilistic Foundations of Spatial Mean-field Models in Ecology and Applications
Denis D. Patterson, Simon A. Levin, A. Carla Staver +1
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between t…
Large fluctuations and growth rates of linear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel i…
On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
In this paper we consider unbounded solutions of perturbed convolution Volterra summation equations. The equations studied are asymptotically sublinear, in the sense that the state…