Search
Skip to Search Results- 2Animal movement
- 2Mathematical ecology
- 2Pattern formation
- 2Stability
- 1Advection–diffusion
- 1Biological control
-
Detecting minimum energy states and multi-stability in nonlocal advection–diffusion models for interacting species
Download2022-06-13
Valeria Giunta, Thomas Hillen, Mark A. Lewis, Jonathan R. Potts
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the...
-
2009
Hillen, T., Lewis, M.A., Lee, J.M.
In this paper, we consider spatial predator–prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and...
-
2015-01-01
Jonathan R. Potts, Mark A. Lewis
Territoriality is a phenomenon exhibited throughout nature. On the individual level, it is the processes by which organisms exclude others of the same species from certain parts of space. On the population level, it is the segregation of space into separate areas, each used by subsections of the...