Related papers: Detecting minimum energy states and multi-stabilit…
We consider a quantum many-body model describing a system of electrons interacting with themselves and hopping from one ion to another of a one dimensional lattice. We show that the ground state energy of such system, as a functional of the…
Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…
Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence,…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…
This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system…
Despite the general acknowledgment of the role of niche and fitness differences in community dynamics, species abundance has been coined as a relevant feature not just regarding niche perspectives, but also according to neutral…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
Determining the relative importance of environmental factors, biotic interactions and stochasticity in assembling and maintaining species-rich communities remains a major challenge in ecology. In plant communities, interactions between…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
We argue that the spatial discretization of the strongly nonlinear Lefever-Lejeune partial differential equation defines a nonlinear lattice that is physically relevant in the context of the nonlinear physics of ecosystems, modelling the…