Abstract
Based on the step function and signum function, a chaotic system which can generate multiscroll chaotic attractors with arrangement of saddle-shapes is proposed and the stability of its equilibrium points is analyzed. The under mechanism for the generation of multiscroll chaotic attractors and the reason for the arrangement of saddle shapes and being symmetric abouty-axis are presented, and the rule for controlling the number of scroll chaotic attractors with saddle shapes is designed. Based on the core chips including Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array and Digital to Analog Converter chip AD9767, the peripheral circuit and the Verilog Hardware Description Language program for realization of the proposed multiscroll chaotic system is constructed and some experimental results are presented for confirmation. The research result shows that the occupation of multipliers and Phase-Locked Loops in Field Programmable Gate Array is zero.
Highlights
Based on Chua’s circuit and using a sinusoidal function, a chaotic system which is capable of generating multiscroll chaotic attractors was proposed and verified by using the hardware circuit with the universal trigonometric converter AD639 in [1]
Combined with the Y values of the two equilibrium points, it can be seen that these two equilibrium points are located obliquely above the equilibrium points S2 and S5, respectively. erefore, the arrangement of these six-scroll chaotic attractor eventually presents a saddle shape and be symmetric about y-axis
In the Quartus II interface, the resources occupied by these multiscroll chaotic systems that can generate saddle-shaped multiscroll chaotic attractors when using the Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array design program are 20% of the logic cells, 19% of pins, and 24% of memory bits
Summary
Since the advent of the Lorenz chaotic system in 1976, the proposal, analysis, control, and synchronization of chaotic systems and their applications and the corresponding educational research have become a hot topic [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. With the rise of digital chaotic secure communication, chaotic systems are widely realized by Digital Signal Processor [23, 24], Field Programmable Gate Array [25,26,27], Advanced RISC Machine [28, 29], Arduino [30, 31], and other digital chips He et al implemented a fractional-order Lorenz hyperchaotic system by using Digital Signal Processor [23]. Based on the Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array and Digital to Analog Converter chip AD9767, the peripheral circuit and Verilog Hardware Description Language program are designed to realize the multiscroll chaotic system for confirmation. Note that (3) and (4) are the definitions of step functions and (5) is the definition of signum function
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
