Related papers: Introduction to population dynamics and resource e…
This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
Competition indices are models frequently used in ecology to account for the impact of density and resource distribution on the growth of a plant population. They allow to define simple individual-based models, by integrating information…
Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. This population is facing an {\it environmental gradient}: to survive at location $x$, an…
In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and…
In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
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…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and educational level, is considered from the point of view of dynamical systems theory. It is shown that there exist…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf…
The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite…
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…