FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points
Abstract
:1. Introduction
- (1)
- We propose a new dissipative chaotic jerk system having three quadratic nonlinear terms.
- (2)
- We establish that the new chaotic jerk system has two unstable equilibrium points, which implies that the new system exhibits a self-excited chaotic attractor.
- (3)
- We carry out a detailed bifurcation analysis of the new jerk system which shows the changes in the dynamic behavior of the jerk system with respect to changes in the system parameters.
- (4)
- We establish that the new jerk system has multistability with coexisting chaotic attractors.
- (5)
- We provide a control application of the new jerk system, viz. complete synchronization of the new jerk systems via backstepping control.
- (6)
- We design an FPGA implementation of the new chaotic jerk system.
2. A New 3-D Jerk System
3. Bifurcation Analysis for the New 3-D Jerk System
3.1. When the Parameter a Varies
3.2. When the Parameter b Varies
3.3. When the Parameter c Varies
4. Multistability of the Jerk System
5. Complete Synchronization of the New Jerk Systems Using Backstepping Control
6. FPGA Implementation of the New Jerk System
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Resources | Used | Util |
---|---|---|
Slice | 134 | 1.01% |
LUTs | 304 | 0.57% |
FFs | 292 | 0.21% |
DSPs | 10 | 3.18% |
Frequency Max | 111 MHz | – |
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Vaidyanathan, S.; Tlelo-Cuautle, E.; Benkouider, K.; Sambas, A.; Ovilla-Martínez, B. FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points. Technologies 2023, 11, 92. https://doi.org/10.3390/technologies11040092
Vaidyanathan S, Tlelo-Cuautle E, Benkouider K, Sambas A, Ovilla-Martínez B. FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points. Technologies. 2023; 11(4):92. https://doi.org/10.3390/technologies11040092
Chicago/Turabian StyleVaidyanathan, Sundarapandian, Esteban Tlelo-Cuautle, Khaled Benkouider, Aceng Sambas, and Brisbane Ovilla-Martínez. 2023. "FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points" Technologies 11, no. 4: 92. https://doi.org/10.3390/technologies11040092