Related papers: Stabilization of Age-Structured Competing Populati…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modeling bias due to simplifying assumptions or unaccounted factors, limiting…
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
Optimal control of harvested population at the edge of extinction in an unprotected area, is considered. The underlying population dynamics is governed by a Kolmogorov-Petrovsky-Piskunov equation with a harvesting term and space-dependent…
We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single and where several predators compete with each other. In this…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
Species augmentation is one of the methods used to promote biodiversity and prevent endangered species loss and extinction. The current work applies discrete-time optimal control theory to two models of species augmentation for…
In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…
When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
We propose a framework to analyze stability for a class of linear non-autonomous hybrid systems, where the continuous evolution of solutions is governed by an ordinary differential equation and the instantaneous changes are governed by a…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
The properties of competition models where all individuals are identical are relatively well-understood; however, juveniles and adults can experience or generate competition differently. We study here less well-known structured competition…
Understanding the behavior of particles in a dispersed phase system via population balances holds fundamental importance in studies of particulate sciences across various fields. Particle behavior, however, is sophisticated as a single…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…