Abstract
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.
Highlights
Nowadays, chaotic systems and their applications attract considerable attention [1,2,3,4]
Self-excited and hidden attractors of such a system are precisely studied in this paper, and to observe chaos in real-time, the analyzed four-dimensional chaotic system is implemented in a FPGA
A four-dimensional chaotic jerk system with specific features was presented in this work
Summary
Chaotic systems and their applications attract considerable attention [1,2,3,4]. Coexisting dynamics in a system can be observed by means of attractors, basin attraction plots, and bifurcation diagrams with initial conditions He et al [47] investigated the complexity of the multiple coexisting fractional-order chaotic systems, and found that that the C0 complexity measure can identify the multistability of the system in the initial condition plane. FPGAs have attracted a lot of interest for use in fast prototyping of different chaotic systems; e.g., for the implementation of memristors [56], high-dimensional [57], physical unclonable functions [58], multi-scroll [59,60], and other chaotic or hyperchaotic systems [61]. Self-excited and hidden attractors of such a system are precisely studied in this paper, and to observe chaos in real-time, the analyzed four-dimensional chaotic system is implemented in a FPGA.
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