**5. Conclusions**

Our work introduces a symmetry nonlinear system with remarkable dynamics. There are only five nonlinear terms in the system, which generates chaos. By considering the initial conditions, we find coexisting attractors in the system verifying its multistability feature. Entropy measurement also indicates the system's complexity. We believe that our work contributes to the known list of chaotic systems with algebraic simplicity. It is possible for us to apply a modified version of such a system to describe turbulent flows [46,47]. We implemented a neural-based approach to predict a system's chaos in short-term. Long-term prediction of such chaotic signals should be considered. In addition, prediction results will be applied to control chaos in our future investigation. In addition, realization of the system for practical chaos-based applications will be studied in our future works.

**Author Contributions:** Data curation, V.V.H.; Formal analysis, V.P.T.; Funding acquisition, M.S.K.; Investigation, V.P.T. and V.V.H.; Methodology, A.O. and V.-T.P.; Project administration, M.S.K.; Resources, V.-T.P.; Software, M.S.K.; Supervision, A.O.; Visualization, V.V.H.; Writing—original draft, V.P.T. and A.O.; Writing—review & editing, V.-T.P. All authors have read and agreed to the published version of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
