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 ebook is to couple the educating 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 equipment, simulation instruments and actual attention to assist the reader achieve an intuitive knowing of the houses of chaotic structures. moment, the "medium" used for actual awareness is the FPGA. those units are hugely parallel architectures that may be configured to achieve various common sense features. therefore, FPGAs may be configured to emulate platforms of differential equations.
Nevertheless maximizing the services of an FPGA calls for the consumer to appreciate the underlying and likewise FPGA layout software program. this can be accomplished by means of the 3rd virtue of this publication: a lab part in every one bankruptcy. the following, readers are requested to test with desktop simulations and FPGA designs, to extra their knowing of thoughts 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.
Read or Download A Route to Chaos Using FPGAs: Volume I: Experimental Observations PDF
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Extra resources for A Route to Chaos Using FPGAs: Volume I: Experimental Observations
We will explore the use of quiver in the lab component of this chapter. Nevertheless, pplane is excellent MATLAB code and is open-source. One is encouraged to explore coding styles used in pplane7. 3 Some Basic Mathematical Concepts 21 50 45 40 35 z 30 25 20 15 10 5 0 −20 −15 −10 −5 0 5 10 x Fig. 11 We obtain the Lorenz butterfly with a different initial condition Fig. 12 pplane7 startup 15 20 22 1 Introduction Fig. 13 pplane7 vector field for a simple mass-spring system (no damping) In addition to the phase plot, pplane plots the vector field of two dimensional systems.
11 We obtain the Lorenz butterfly with a different initial condition Fig. 12 pplane7 startup 15 20 22 1 Introduction Fig. 13 pplane7 vector field for a simple mass-spring system (no damping) In addition to the phase plot, pplane plots the vector field of two dimensional systems. As the name implies, a vector field associates a vector to every point in phase space. How do we know the direction of the vector? The answer is we can obtain the direction of the vector from the differential equation. Consider the following system of two dimensional nonlinear ODEs.
46) then Eq. 44) is zero by virtue of Eqs. 43). However, the signum function is nonlinear. 39) shows that signum returns the sign of the input number x: −1 if x is negative, 0 if x is zero and 1 if x is positive. Sketch the signum function or use a few counter-examples to convince yourself that signum is nonlinear. Thus, Eq. 44) may not be zero. 2 is not satisfied and this implies that our system is nonlinear. The point to be noted from this example is that a rigorous proof of nonlinearity may involve a bit of work.