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Motivating by the China's five element philosophy (CFEP) we construct a permuted Volterra quadratic stochastic operator acting on the four dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution…
We consider a four-parameter family of non-Volterra operators defined on the two-dimensional simplex and show that, with one exception, each such operator has a unique fixed point. Depending on the parameters, we establish the type of this…
In this paper, we initiate the study of a discrete-time dynamical system modelling a trophic network connecting the three types of plankton (phytoplankton, zooplankton, mixoplankton) and bacteria. The nonlinear operator V associated with…
We introduce a notion of $\ell$-Volterra quadratic stochastic operator defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. The $\ell$-Volterra operator is a Volterra operator iff $\ell=m$. We study structure of the set of…
Recently, continuous-time dynamical systems, based on systems of ordinary differential equations, for mosquito populations are studied. In this paper we consider discrete-time dynamical system generated by an evolution quadratic operator of…
In the present paper, we consider a convex combination of non-Volterra quadratic stochastic operators defined on a finite-dimensional simplex depending on a parameter $\alpha$ and study their trajectory behaviors. We showed that for any…
We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex $S^{m-1}$. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system…
In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except…
We consider a four-parametric $(a, b, \alpha, \beta)$ family of Volterra quadratic stochastic operators for a bisexual population (i.e., each organism of the population must belong either to the female sex or the male sex). We show that…
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show…
In this paper we study dynamical systems generated by an evolution operator of a dioecious population. This evolution operator is a six-parametric, non-linear operator mapping $[0,1]^2$ to itself. We find all fixed points and under some…
In this paper we consider a population consisting of two species, dynamics of which is defined by a quadratic stochastic operator with variable coefficients, making it discontinuous operator at two points. This operator depends on three…
We consider $\ell$-Volterra quadratic stochastic operators defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. Under some conditions on coefficients of such operators we describe Lyapunov functions and apply them to obtain…
In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In…
In this short note we study a dynamical system generated by a two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution operator of the frequencies of gametes in a two-locus system. We find the set of…
Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the…
The limit behavior of trajectories of dissipative quadratic stochastic operators on a finite-dimensional simplex is fully studied. It is shown that any dissipative quadratic stochastic operator has either unique or infinitely many fixed…
In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on a parameter $\alpha$ and study their trajectory behaviors. We find all fixed points for a non-Volterra quadratic stochastic operator on a…
In this paper, we study a discrete-time dynamical system generated by the evolution operator of a wild mosquito population with specific rates of birth and emergence from larvae to adults. The death rates of larvae and adults are assumed to…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…