Explosive route to chaos through a fractal torus in a generalized Lotka- Volterra model
This paper is an informal treatment of the model \[ x'=x-xy+cx^ 2- azx^ 2,\quad y'=-x+xy,\quad z'=-bz+azx^ 2 \] where a,b,c\(\geq 0\). The authors call this a two-predator one -prey Lotka-Volterra system. Note that in the absence of predation prey grows to infinity. Stability of equilibria and bifurcations are discussed and computer simulations presented. The authors state that at \(b/a=1\) the system jumps into chaos through the birth of a fractal torus.
non-transversal saddle connection type bifurcation
two-predator one -prey Lotka-Volterra system
scientific article; zbMATH DE number 4095270
scientific article