Related papers: Pattern Formation in Mesic Savannas
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold…
Concerns about biodiversity and the long-term stability of forest ecosystems have lead to changing attitudes with respect to plantations. These artificial communities are ubiquitous, yet provide reduced habitat value in comparison to their…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…
Inspired by real scenarios in Northern Patagonia, we analyze a mathematical model of a simple trophic web with two herbivores and one predator. The studied situations represent a common practice in the steppes of Argentine Patagonia, where…
Understanding the causes and effects of spatial vegetation patterns is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous systems to include the effects of spatial heterogeneities.…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…