Functions and Analysis


Generation of Frequency Controlled Chaotic Signals using Ramanujan Theta Function

Authors: Sai Venkatesh Balasubramanian

The present work purports to a signal based generation of chaos, thereby offering a radically innovative solution to the issues of tunability caused in conventional system based chaos generation circuits. Specifically, the Ramanujan Theta Function is seen to represent the output signal of a coupled nonlinear system with two driving signals. Using this concept, the iterative map of the Ramanujan Theta Function is developed using the frequency ratio of driving signals as the control parameter, and the ratio dependent dynamics are studied using the bifurcation plot. The proposed system is implemented in hardware using FPGA and the presence of chaos is validated qualitatively using phase portraits and quantitatively using Lyapunov Exponents, whose trend indeed agree with the one observed in the bifurcation plot. The innovative perspective of signal based chaos proposed using the Ramanujan Theta Function enables easy tunability in chaotic generation systems and this forms the novelty of the present work.

Comments: 6 Pages.

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Submission history

[v1] 2015-10-25 08:11:52

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