Related papers: A Computer-Assisted Study of Red Coral Population …
The reduction in coral reef densities, characterized by the proliferation of macroalgae, has emerged as a global threat. In this paper, we present a discrete-time coral reef dynamical model that incorporates macroalgae. We explore all…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterising spatio-temporal data and understanding how changes at the local scale affect global…
Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
Coral reefs are crucial to marine biodiversity and rely on a delicate symbiotic relationship between corals and zooxanthellae algae. Water temperature variations, however, disrupt this association, leading to coral bleaching events that…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
Ocean acidification is a threat to deep-sea corals and could lead to dramatic and rapid loss of the reef framework habitat they build. Weakening of structurally critical parts of the coral reef framework can lead to physical habitat…
Coral reefs are increasingly subjected to major disturbances threatening the health of marine ecosystems. Substantial research underway to develop intervention strategies that assist reefs in recovery from, and resistance to, inevitable…
In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
I present a simple numerical model based on iteratively updating subgroups of a population, individually modeled by nonnegative real numbers, by a constant decay factor; however, at each iteration, one group is selected to instead be…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
Critical transitions describe sudden changes in the state of an ecosystem. In classical bifurcation theory, such transitions occur when the value of a parameter exceeds a threshold (``bifurcation") value. More recently, critical transitions…
We study the evolution of the rotation frequency for accreting compact stars. The discontinuous change of the moment of inertia of a rapidly rotating star due to the possible quark core appearance entails a characteristic change in the spin…
The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of…
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…