"Battle of the sexes" is the title of Chapter 9 in Richard Dawkins' Selfish Gene, in which he advocated the gene-centered view of evolution.  The central thesis is that an organism is expected to evolve to maximize the number of copies of its genes passed on globally, and as a result, populations will tend towards an evolutionarily stable strategy (ESS).  The concept of ESS was introduced by John Maynard Smith, in collaboration with George R. Price.  They used the branch of mathematics called "game theory" to understanding the logic of animal conflict.  Dawkins took their method of analyzing aggresive contests among animals of the same species and applied it to sex; he found a stable proportion of males and females playing some hypothetical strategies.  In the second edition of Selfish Gene, Dawkins acknowledged a misstatement, based on Peter Schuster and Karl Sigmund's differential equations corresponding to Dawkins' game.  The ratio Dawkins found was not asymptotically stable, but oscillatory.  This worksheet utilizes Maple's LinearAlgebra, VectorCalculus, DEtools packages, in addition to other basic commands, to investigate the type and stability of the fixed point of the equations by Schuster and Sigmund. This example serves to supplement the topic "nonlinear differential equations and stabilities" covered in standard undergraduate textbooks such as that by W. E. Boyce and R. C. DiPrima.