**Vo Phu Thoai 1, Maryam Shahriari Kahkeshi 2, Van Van Huynh 3, Adel Ouannas <sup>4</sup> and Viet-Thanh Pham 5,\***


Received: 19 April 2020; Accepted: 22 May 2020; Published: 25 May 2020

**Abstract:** Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We discovered the system's rich behavior such as chaos through phase portraits, bifurcation diagrams, Lyapunov exponents, and entropy. Interestingly, multi-stability was observed when changing system's initial conditions. Chaos of such a system was predicted by applying a machine learning approach based on a neural network.

**Keywords:** chaos; symmetry; entropy; prediction
