Related papers: Stabilization of Age-Structured Competing Populati…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of…
The classical two-species non-linear Predator-Prey system, often used in population dynamics modeling, is expressed in terms of a single positive coupling parameter $\lambda$. Based on standard logarithmic transformations, we derive a novel…
Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting…
In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles.…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric…
In this paper, we extend the demographic eco-evolutionary game approach, based on explicit birth and death dynamics instead of abstract "fitness" interpreted as an abstract "Malthusian parameter", by the introduction of the delay resulting…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…
This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species: prey, predator, and food for the…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
Structure, composition and stability of ecological populations are shaped by the inter- and intra-species interactions within these communities. It remains to be fully understood how the interplay of these interactions with other factors,…
In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (SIR)…