A SIMPLE SMOOTH CHAOTIC SYSTEM WITH A 3-LAYER ATTRACTOR

This Letter reports a simple smooth quadratic autonomous chaotic system with four unstable equilibrium points and three homoclinic orbits, and can display a 3-layer attractor among some others. It is the first example of a simple smooth quadratic system that we know, which can exhibit Šhilnikov chaos without numerical evidence of a route to chaos through period-doubling bifurcations.