Dynamics Analysis of a Three-Dimensional Nonlinear System with No or Infinite Equilibria

A three-dimensional nonlinear system with six terms and three varying parameters is investigated in this paper. The system has no any equilibrium point within a wide range of parameters. The system can also have infinite equilibrium points which locate on a straight line. Basic dynamical behaviors of the nonlinear system are analyzed by employing bifurcation diagrams and time series. Stability of the system can be determined by two varying parameters under the condition of a fixed parameter. Another nonlinear system with a symmetrical parameter is also investigated. A problem on switching control of two systems is discussed simply by numerical simulations.