Related papers: Poincar\'e map construction for some classical two…
The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…
Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…
For a polynomial p with a repelling fixed point w, we consider Poincar\'{e} functions of p at w, i.e. entire functions L which satisfy L(0)=w and p(L(z))=L(p'(w)*z) for all z in the complex plane. We show that if the component of the Julia…
Given a subspace arrangement, there are several De Concini-Procesi models associated to it, depending on distinct sets of initial combinatorial data (building sets). The first goal of this paper is to describe, for the root arrangements of…
We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A…
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…
We study a class of 2-dimensional Hamiltonian systems $H(x,y,p_x,p_y)=\frac12(p_x^2+p_y^2) +V(x,y)$ in which the plane $x$=$p_x$=0 is invariant under the Hamiltonian flow, so that straight-line librations along the y axis exist, and we also…
When faced with an imminent risk of predation, many animals react to escape consumption. Antipredator strategies are performed by individuals acting as a group to intimidate predators and minimize the damage when attacked. We study the…
In the framework of Lotka-Volterra dynamics with evolutionary parameter variation, it is shown that a system of two competing species which is evolutionarily unstable, if left to themselves, is stabilized by a commmon predator preying on…
We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: $(1)$ prey movement follows a nonlinear diffusion, $(2)$ preys have a refuge zone (sometimes called "protection zone") where predators cannot…
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…
This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type…
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…
In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered - with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the…
We present log-linear dynamical systems, a dynamical system model for positive quantities. We explain the connection to linear dynamical systems and show how convex optimization can be used to identify and control log-linear dynamical…
In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
Current evolutionary theory suggests that many natural signaling systems evolved from preexisting cues. In aposematic systems, prey warning signals benefit both predator and prey. When the signal is highly beneficial, a third species often…
Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species. The existence and stability of the equilibria of…
We discuss the problem of Poincare recurrences in area-preserving maps and the universality of their decay at long times. The work is related to to the results presented in Refs. [1,2].