Functions and Analysis


Nonlinear Dynamics and Chaos in Third Order Mock Theta Functions

Authors: Sai Venkatesh Balasubramanian

The present work purports to the generation of a signal based chaos based on Ramanujan’s Mock Theta Functions. Specifically, the variable in these functions is viewed as an additively coupled sum of sinusoidal signals, with competing frequencies. Thus, by adapting the seven third order mock theta functions into signals, the derivatives are computed and used to form the corresponding iterative maps, which are studied using phase portraits. It is seen that the phase portraits of three of the seven forms exhibit rich, ornamental patterns, characteristic of chaos. Using these, the bifurcation diagrams are plotted, and the chaotic behavior is quantitatively characterized using Lyapunov Exponent and Kolmogorov Entropy. It is seen that the nature of chaos in the mock theta form based signals indeed depend on the frequency ratio of the driving signals, thus pertaining to a case of signal based chaos, which has the key advantage of easy tunability, which forms the novelty of the present work.

Comments: 8 Pages.

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Submission history

[v1] 2015-10-28 20:16:06

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