Perfect harmony: The discrete dynamics of cooperation
The paper studies the dynamical system \[ x_{n+1}=x_ n\exp (r(1-x_ n)+sy_ n),\quad y_{n+1}=y_ n\exp (r(1-y_ n)+sx_ n),\quad n=0,1,2,... \] with positive \(r,s,x_ 0,y_ 0\), and in particular its stretching and folding actions and its Hopf bifurcations. Also an approximating version with truncated Taylor series for both \(e^{sy_ n}\) and \(e^{sx_ n}\) is studied. The paper ends with a report on extensive computer simulations, including a bifurcation diagram describing the evolution from a stable attracting circle to a presumed strange attractor.
scientific article; zbMATH DE number 4207830