Chaos, bifurcation, coexisting attractors and circuit design of a three-dimensional continuous autonomous system

This letter investigates the complex dynamical behaviors of a three-dimensional continuous autonomous system which is described as x˙=ax−yz,y˙=−by+xz,z˙=−cz+x2. Some new results are presented by further research. The chaos and bifurcation of the system are analyzed. It proves that the system occurs double Hopf bifurcation at the equilibria. Also, study shows that the system coexist multiple attractors including point attractors, periodic attractors and chaotic attractors. Electronic circuit is also designed for realizing the chaos of the system.