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U. U. Jamilov

Publications and source records attributed to U. U. Jamilov.

6 recordsLinked to original sources
arXiv2022

A family of non-Volterra quadratic operators corresponding to permutations

In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on a parameter $α$ and study their trajectory behaviors. We find all fixed points for a non-Volterra quadratic stochastic operator on a finite-dimensional simplex. We construct some Lyapunov functions. A complete description of the set of limit points is given, and we show that such operators have the ergodic property.

math.DS↗
arXiv2018

On Volterra quadratic stochastic operators of a two-sex population on $S^1\times S^1$

We consider a four-parametric $(a, b, α, β)$ 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 independently on parameters each such operator has at least two fixed points. Moreover, under some conditions on parameters the operator has infinitely many (continuum) fixed points. Choosing parameters, numerically we show that a fixed point may be any type: attracting, repelling, saddle and non-hyperbolic. We separate five subfamilies of quadratic operators and show that each operator of these subfamilies is regular, i.e. any trajectory constructed by the operator converges to a fixed point.

math.DS↗
arXiv2014

On the Random Dynamics of Volterra Quadratic Operators

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 almost surely converge to one of the vertices of the simplex $S^{m-1}$ implying the survival of only one species. We also show that the minimal random point attractor of the system equals the set of all vertices. The convergence proof relies on a martingale-type limit theorem which we prove in the appendix.

math.DS↗
arXiv2013

(G,μ)- Quadratic Stochastic Operators

We consider a new subclass of quadratic stochastic (evolutionary) operators on the simplex indexed by a finite Abelian group G with heredity law μ. With the help of the notion of s(μ)-invariant subgroups, where s(μ) denotes the support of μin G, we prove that almost all (w.r.t.\ Lebesgue measure) trajectories of such operators converge to a unique fixed point which is the center of the simplex. We also identify and describe the periodic trajectories of the operator and give conditions for regularity and periodicity.

math.DS↗
arXiv2006

On $F$-Quadratic Stochastic Operators

In this paper we introduce a notion of $F-$ quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the $F$-quadratic stochastic operator converges to the fixed point exponentially fast.

math.DS↗