Sigmund, Karl A survey of replicator equations. (English) Zbl 0606.92001 Complexity, language, and life: math. approaches, Biomath. 16, 88-104 (1986). [For the entire collection see Zbl 0572.00025.] Replicator equations are ordinary differential equations on the unit simplex for which the boundary faces are invariant. Such equations occur in many places, e.g. genetics, ecology, chemical kinetics and game dynamics. This paper offers a survey of the mathematical results concerned with the existence of periodic orbits, the convergence of time averages, permanence and extinction, the validity of maximum principles etc... Cited in 1 ReviewCited in 8 Documents MSC: 92B05 General biology and biomathematics Keywords:limit cycles; gradient systems; Replicator equations; ordinary differential equations on the unit simplex; survey; existence of periodic orbits; convergence of time averages; permanence; extinction; validity of maximum principles Citations:Zbl 0572.00025 PDFBibTeX XML