By Bharathwaj Muthuswamy, Santo Banerjee
The objective of this introductory ebook is to couple the educating of chaotic circuit and platforms idea 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 awareness to aid the reader achieve an intuitive realizing 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 achieve various common sense features. for this reason, FPGAs might be configured to emulate structures of differential equations.
Nevertheless maximizing the features of an FPGA calls for the consumer to appreciate the underlying and likewise FPGA layout software program. this is often completed by means of the 3rd virtue of this ebook: a lab part in each one bankruptcy. right here, readers are requested to test with desktop simulations and FPGA designs, to additional their knowing of options coated within the book.
This textual content is meant for graduate scholars in technological know-how 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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Additional resources for A Route to Chaos Using FPGAs: Volume I: Experimental Observations
3 Some Basic Mathematical Concepts We will start with the very basic concept of what is a linear system (and what is not). 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).
For example consider the volume knob on your car stereo. This volume knob adjusts the gain of your audio amplifier. In other words the audio amplifier multiplies your input signal by a factor proportional to how much you turn the volume knob. Mathematically, the audio amplifier transforms an input function into another output function. Hence we have our first definition . 1 A system is a function whose domain and range are sets of signals called signal spaces. For example, let us say the audio amplifier has a gain K ∈ R that can be controlled by the volume knob.
87) Construct a three dimensional phase plot in MATLAB. 10 In the text, we considered three dimensional systems. Now consider the following four dimensional system proposed by R¨ossler . 92) α, β, γ , δ ∈ R are parameters. What are the equilibrium points for this system? Simulate the system in MATLAB, try to pick values for α, β, γ , δ for chaos. Contrast the behavior of this system with the R¨ossler system in Eqs. 78). The system above is the first example of a hyperchaotic system. 11 In the text, we discussed “robustness” of the Lorenz attractor.
A Route to Chaos Using FPGAs: Volume I: Experimental Observations by Bharathwaj Muthuswamy, Santo Banerjee