Journal
SYMMETRY-BASEL
Volume 12, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/sym12040569
Keywords
four-dimensional chaotic systems; hidden attractors; self-excited attractors; complexity analysis; FPGA implementation
Categories
Funding
- Key research and development plan of Shaanxi Province [2018GY-091]
- talent foundation of Xijing University [XJ19B03]
- Natural Science Foundation of China [61901530, 11747150]
- China Postdoctoral Science Foundation [2019M652791]
- Postdoctoral Innovative Talents Support Program [BX20180386]
- Ministerio de Ciencia, Innovacion y Universidades from Spain [PGC2018-097198-B-I00]
- Fundacion Seneca de la Region de Murcia from Spain [20783/PI/18]
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In the present work, a new nonequilibrium four-dimensional chaotic jerk system is presented. The proposed system includes only one constant term and has coexisting and hidden attractors. Firstly, the dynamical behavior of the system is investigated using bifurcation diagrams and Lyapunov exponents. It is illustrated that this system either possesses symmetric equilibrium points or does not possess an equilibrium. Rich dynamics are found by varying system parameters. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Then, coexisting and hidden chaotic attractors are observed, and basin attraction is plotted. Moreover, using the multiscale C0 algorithm, the complexity of the system is investigated, and a broad area of high complexity is displayed in the parameter planes. In addition, the chaotic behavior of the system is studied by field-programmable gate array implementation. A novel methodology to discretize, simulate, and implement the proposed system is presented, and the successful implementation of the proposed system on FPGA is verified through the simulation outcome. Finally, a robust sliding mode controller is designed to suppress the chaotic behavior of the system. To deal with unexpected disturbances and uncertainties, a disturbance observer is developed along with the designed controller. To show the successful performance of the designed control scheme, numerical simulations are also presented.
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