A Nonlinear Five-Term System: Symmetry, Chaos, and Prediction
Vo Phu Thoai,
Maryam Shahriari Kahkeshi,
Van Van Huynh,
Adel Ouannas,
Viet-Thanh Pham
Affiliations
Vo Phu Thoai
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Maryam Shahriari Kahkeshi
Faculty of Engineering, Shahrekord University, Shahrekord 64165478, Iran
Van Van Huynh
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Adel Ouannas
Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Laarbi Tebessi, Tebessa 12002, Algeria
Viet-Thanh Pham
Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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.
