Related papers: A Regular Gonosomal Evolution Operator with uncoun…

We consider a population with two equal dominated species, dynamics of which is defined by one-dimensional piecewise-continuous, two parametric functions. It is shown that for any non-zero parameters this function has two fixed points and…

We introduce the gonosomal algebra. Gonosomal algebra extend the evolution algebra of the bisexual population (EABP) defined by Ladra and Rozikov. We show that gonosomal algebras can represent algebraically a wide variety of sex…

We study the dynamics of the renormalization operator acting on the space of pairs (v,t), where v is a diffeomorphism and t belongs to [0,1], interpreted as unimodal maps x-->v(q_t(x)), where q_t(x)=-2t|x|^a+2t-1. We prove the so called…

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…

This paper studies locally linear involutions on S^4. Our main theorem shows that any such involution with a 1-dimensional fixed-point set is necessarily linear, provided the fixed-point set admits an equivariant tubular neighborhood. The…

We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…

An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…

In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…

In this work, we consider a continuous dynamical system associated with the fixed point set of a nonexpansive operator which was originally studied by Bo\c{t} & Csetnek (2015). Our main results establish convergence rates for the system's…

We describe fixed points of an infinite dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values on the Cayley tree. This operator is defined by a countable set of parameters…

We study the ``renormalization group action'' induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…

Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…

$\beta(1,0)$-trees provide a convenient description of rooted non-separable planar maps. The involution $h$ on $\beta(1,0)$-trees was introduced to prove a complicated equidistribution result on a class of pattern-avoiding permutations. In…

In this paper we present some local dynamic bifurcation results in terms of invariant sets of nonlinear evolution equations. We show that if the trivial solution is an isolated invariant set of the system at the critical value…

We extend to binary relational systems the notion of compact and normal structure, introduced by J.P.Penot for metric spaces, and we prove that for the involutive and reflexive ones, every commuting family of relational homomorphisms has a…

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…

In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a…

In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-like…