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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 θ$$ \theta $$ and study their trajectory behaviors. We showed that in the case m=3$$ m=3 $$ depending on the parameter θ∈[0,1]$$ \theta \in \left[0,1\right] $$ and an initial point, the trajectories of such operator converge to a fixed point. For m≥4$$ m\ge 4 $$, any trajectory of the operator converges to the center of the simplex. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the structure of genetic algebras associated with permuted Lotka-Volterra operators on a finite-dimensional simplex. Furthermore, three dimensional permuted Lotka-Voltarra algebras are considered and the description of their derivations are given as well. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the stability of a class of nonlinear stochastic operators on a finite‐dimensional simplex. We identify a number of properties of the set of the class of stochastic operators, including the stability of each operator. We then use these operators to define non‐homogeneous Markov measures that rely on initial data and carry out an investigation into the absolute continuity and singularity of these measures. [ABSTRACT FROM AUTHOR]

We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems. [ABSTRACT FROM AUTHOR]

We consider Volterra and non-Volterra cubic stochastic operators. For a Volterra cubic stochastic operator defined on the two-dimensional simplex, it is shown that the vertices and the centre of the simplex are fixed points. The trajectory of such an operator starting from any point from the boundary of the simplex is convergent, and the trajectory of such an operator starting from any point from the interior of the simplex except the centre does not converge. Moreover, therein proven the mean of any trajectory does not converge. For a non-Volterra cubic stochastic operator defined on the two-dimensional simplex, it is proved that the uniqueness of a fixed point, which is repelling and any trajectory starting from the boundary of the simplex converges to a periodic trajectory which consists of three vertices of the simplex. The set of limit points of the trajectory starting from the interior of the simplex except the centre is an infinite subset of the boundary of the simplex. [ABSTRACT FROM AUTHOR]

Iii the present paper. we consider discrete-time dynamical systems generated by Lotka-Volterra operators. We showed that any trajectory of the system diverges and moreover the time averages also do not converge. [ABSTRACT FROM AUTHOR]