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

By Bharathwaj Muthuswamy, Santo Banerjee

The objective of this introductory booklet is to couple the instructing of chaotic circuit and platforms conception with using box programmable gate arrays (FPGAs).

As such, it differs from different texts on chaos: first, it places emphasis on combining theoretical equipment, simulation instruments and actual attention to aid the reader achieve an intuitive figuring out of the houses of chaotic structures. 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 capabilities. as a result, FPGAs might be configured to emulate structures of differential equations.

Nevertheless maximizing the services of an FPGA calls for the person to appreciate the underlying and likewise FPGA layout software program. this can be completed via the 3rd virtue of this ebook: a lab part in each one bankruptcy. the following, readers are requested to scan with machine simulations and FPGA designs, to additional their knowing of techniques coated within the book.

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

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A Route to Chaos Using FPGAs: Volume I: Experimental Observations

The aim of this introductory e-book is to couple the instructing of chaotic circuit and platforms concept with using box programmable gate arrays (FPGAs). As such, it differs from different texts on chaos: first, it places emphasis on combining theoretical equipment, simulation instruments and actual awareness to assist the reader achieve an intuitive figuring out of the homes of chaotic platforms.

Additional info for A Route to Chaos Using FPGAs: Volume I: Experimental Observations

Sample text

In Chap. 5, we will simplement chaotic DDEs. However most physical systems cannot be solved explicitly. But, interestingly, we can predict the behavior of most physical systems without solving for an explicit closed form solution. An introduction to this approach is the topic of Sect. 3. 3 Fixed (Equilibrium) Points Consider the differential equation in Eq. 53), written explicitly using time t: dx = cos(x(t)) dt Physically, points of interest are x † for which the derivative x †. 53) dx dt x † = 0.

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. 18. Once you download the online design to the DE2-115 board, you will notice that the base design clock is counting much faster than the usual 1 Hz frequency for a seconds counter.

2. 8. 3. Numerically simulate the system using MATLAB and display phase plots. Start with initial conditions near the equilibrium points. 4. The phase plot will qualitatively describe system behavior. Use the phase plot as a starting point for rigorous analysis. The beauty of the equilibrium point method lies in the fact that we do not find an explicit analytic solution. Rather, we determine any equilibrium points and determine system behavior by starting close to those equilibrium points. An example application of the equilibrium point method was the Lorenz system.

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