A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability
In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlineari...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/4/612 |
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| author | Othman Abdullah Almatroud Karthikeyan Rajagopal Viet-Thanh Pham Giuseppe Grassi |
| author_facet | Othman Abdullah Almatroud Karthikeyan Rajagopal Viet-Thanh Pham Giuseppe Grassi |
| author_sort | Othman Abdullah Almatroud |
| collection | DOAJ |
| description | In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system’s dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system’s basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system. |
| first_indexed | 2024-03-07T22:22:32Z |
| format | Article |
| id | doaj.art-203b949cfa7749538dbad5545cd999e3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-07T22:22:32Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-203b949cfa7749538dbad5545cd999e32024-02-23T15:26:17ZengMDPI AGMathematics2227-73902024-02-0112461210.3390/math12040612A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and StabilityOthman Abdullah Almatroud0Karthikeyan Rajagopal1Viet-Thanh Pham2Giuseppe Grassi3Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaCentre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, IndiaFaculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, VietnamDipartimento Ingegneria Innovazione, Universitá del Salento, 73100 Lecce, ItalyIn nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system’s dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system’s basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system.https://www.mdpi.com/2227-7390/12/4/612chaotic systemmultistabilitystability |
| spellingShingle | Othman Abdullah Almatroud Karthikeyan Rajagopal Viet-Thanh Pham Giuseppe Grassi A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability Mathematics chaotic system multistability stability |
| title | A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability |
| title_full | A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability |
| title_fullStr | A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability |
| title_full_unstemmed | A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability |
| title_short | A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability |
| title_sort | novel chaotic system with only quadratic nonlinearities analysis of dynamical properties and stability |
| topic | chaotic system multistability stability |
| url | https://www.mdpi.com/2227-7390/12/4/612 |
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