In this thesis a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations is presented and further studied , which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Dynamical behaviors of this new chaotic system, including some basic dynamical properties, bifurcations, periodic windows, routes to chaos, compound structures of the new attractors and their connections, etc. have been investigated both theoretically and numerically
