Analysis of a three-dimensional quadratic smooth continuous dissipative chaotic system with two equilibria

A simple three-dimensional smooth chaotic system with four quadratic terms is constructed. A chaotic attractor can be generated from the system with two equilibria and seven parameters. Basic dynamical behaviors including equilibria, dissipation, state response, Lyapunov exponents, Lyapunov dimension and variation of parameters are investigated. Finally, the chaotic system is also controlled better by designing simple linear state feedback controllers.