content_image/297242.jpg content_image/297241.jpg
We depict in Figure 4 the z$_{3}$ − coordinate of the solution of (6.16) with z$_{1}$ ( ζ$_{0}$ ) = 0 . 53 , z$_{2}$ ( ζ$_{0}$ ) = 0 . 57 , z$_{3}$ ( ζ$_{0}$ ) = − 1 . 51 , where ζ$_{0}$ = 0 . 4 . Moreover, the trajectory of the same solution is represented in Figure 5. 

The simulations shown in Figures 4 and 5 support Theorem 2.2 such that the Poincaré chaos of system (6.11) is extended by (6.16). 

## 7 Conclusion 

<img src='content_image/297242.jpg'>

<img src='content_image/297241.jpg'>

In our previous paper [2] we developed the concept of Poisson stable points to unpredictable ones, which imply the Poincaré chaos in the quasi-minimal set. This new definition makes homoclinic chaos and the late descriptions of the phenomenon be closer to each other such that a unified background of chaos can be obtained in the future. Besides, in article [3], an unpredictable function was defined as an unpredictable point of the Bebutov dynamical system. In the present paper, we have obtained samples of unpredictable functions and sequences, which are in the basis of Poincaré chaos. The unpredictable sequences are utilized in the construction of piecewise continuous functions, and such functions in their own turn are utilized for the construction of continuous unpredictable functions. Thus, one can claim that the basics 

