This paper describes the irregular behavior of solutions to certain differential equations. This phenomenon is called chaos and in ordinary automomous differential equations it occurs beyond three dimensions when represented by normal type. The authors propose here a new differential equation, called the manifold piecewise linear system, in dealing with this phenomenon. The equation is described by special coupling of the linear system and, from the local solution rigorously obtained, a Poincare map for investigation of the solution behaviors is calculated rigorously. Thus, an analytical approach to the chaos of differential equations which cannot be dealt with at the present becomes possible. The differential equation solution is shown in a certain parameter region to become aperiodic and is neither convergent nor divergent. This equation can be analyzed as a whole by the Poincare map in terms of the different parameters with the same form. This is desirable for sensitivity analysis. Also, for a given parameter and region of definition, Poincare maps are expressed in terms of different forms and an example corresponding to previous research is presented.