Cards of fixed points of some Lotka-Volterra operators

Abstract

The paper considers a special type of the Lotka-Volterra operator operating in a four-dimensional simplex. The tournament corresponding to this operator has four cyclic triples. All kinds of fixed point cards are built for it. It is proved which types of cards exist for Lotka-Volterra operators in the general position, and which cannot be. The paper also proposes a new approach to constructing an oriented card of fixed points.

Keywords

• lotka-volterra operator
• card of fixed points
• skew-symmetric matrix
• graph
• hamilton cycle
• tournament