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

By Bharathwaj Muthuswamy, Santo Banerjee

The function of this introductory publication is to couple the instructing of chaotic circuit and structures 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 consciousness to aid the reader achieve an intuitive knowing of the houses of chaotic platforms. moment, the "medium" used for actual cognizance is the FPGA. those units are hugely parallel architectures that may be configured to gain numerous good judgment capabilities. for this reason, FPGAs may be configured to emulate structures of differential equations.

Nevertheless maximizing the services of an FPGA calls for the person to appreciate the underlying and in addition FPGA layout software program. this is often accomplished through the 3rd virtue of this e-book: a lab part in every one bankruptcy. right here, readers are requested to scan with desktop simulations and FPGA designs, to extra their knowing of thoughts lined 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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Additional info for A Route to Chaos Using FPGAs: Volume I: Experimental Observations

Example text

This will eventually help us understand what kind of systems give rise to chaotic behaviour. 1 Linear Versus Nonlinear Equations Consider Eqs. 16) What are the solutions to Eqs. 16)? To answer this question notice that Eq. 16) can be simplified to x − 3y = 3. Thus we have only one equation in two unknowns, shown below. 17) y = −1 3 Hence if we let x ∈ R, there are infinitely many real number solutions in the form (x, y). In other words, we have two superimposed straight lines in our solution space.

16) What are the solutions to Eqs. 16)? To answer this question notice that Eq. 16) can be simplified to x − 3y = 3. Thus we have only one equation in two unknowns, shown below. 17) y = −1 3 Hence if we let x ∈ R, there are infinitely many real number solutions in the form (x, y). In other words, we have two superimposed straight lines in our solution space. 2 plots one of the equations, the result is Fig. 10. The beauty of linear equations is that we can have only two other kinds of solutions to a system of linear equations: a unique solution or no solution.

The answer is: no. This situation is very common when interfacing to external devices. For example, if our design were to interface with external memory (like SDRAM) then we will most likely have our FPGA design running at one frequency while the external SDRAM’s clock is at a different frequency. Nevertheless we should clearly separate the different clock domains in our design. If we do, then we can utilize powerful timing closure tools provided by FPGA manufacturers to ensure that our design meets timing requirements.

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