A Route to Chaos Using FPGAs: Volume I: Experimental by Bharathwaj Muthuswamy, Santo Banerjee

By Bharathwaj Muthuswamy, Santo Banerjee

The goal of this introductory publication is to couple the instructing of chaotic circuit and structures thought with using box programmable gate arrays (FPGAs).

As such, it differs from different texts on chaos: first, it places emphasis on combining theoretical tools, simulation instruments and actual consciousness to aid the reader achieve an intuitive knowing of the homes of chaotic platforms. moment, the "medium" used for actual consciousness is the FPGA. those units are vastly parallel architectures that may be configured to achieve various common sense features. therefore, FPGAs should be configured to emulate structures of differential equations.

Nevertheless maximizing the functions of an FPGA calls for the consumer to appreciate the underlying and likewise FPGA layout software program. this is often accomplished by means of the 3rd virtue of this e-book: a lab part in each one bankruptcy. right here, readers are requested to scan with computing device simulations and FPGA designs, to extra their realizing of ideas lined within the book.

This textual content is meant for graduate scholars in technology and engineering attracted to exploring implementation of nonlinear dynamical (chaotic) structures on FPGAs.

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1 below is a sample VHDL hardware specification. 1 Combinational logic in VHDL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -- Lines starting with -- are comments in VHDL. all; entity simpleLogicGates is port ( x1,x2,x3 : in std_logic; x : in std_logic_vector(3 downto 0); y : out std_logic_vector(4 downto 0)); end simpleLogicGates; architecture combinational of simpleLogicGates is begin y(0) <= (x1 and x2) or x3; y(2 downto 1) <= (x1&x(0)) AND (x2&x(1)); y(4 downto 3) <= x(3 downto 2); end combinational; The first three statements are IEEE standardized libraries to facilitate synthesis [6].

Nature 120:363–364 6. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141 7. Matsumoto T (1984) A chaotic attractor from Chua’s circuit. IEEE Trans Circuits Syst CAS 31(12):1055–1058 8. Chua LO (2011) Chua’s circuit. In: Scholarpedia. org/article/Chua_ circuit. Accessed 25 Dec 2012 9. Muthuswamy B et al (2009) A Synthetic inductor implementation of Chua’s circuit. In: University of California, Berkeley, EECS Technical Reports. html. Accessed 22 Nov 2014 10. Sprott JC (2010) Elegant chaos.

44 2 Designing Hardware for FPGAs Fig. 17 System with a single synchronous clock. Each module uses a single pulse generator that has an enable pulse that is exactly 20 ns wide. This pulse acts as a synchronous trigger input for the subsequent module Reset Seconds Counter pulseOut clockIn Reset enableIn Minutes Counter pulseOut clockIn Reset enableIn Hours Counter clockIn One way to visualize an FSM is using State Machine Diagrams. The state transition diagram for the single pulse generator is shown in Fig.

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