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.

Download: PDF

Submission history

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

Unique-IP document downloads: 81 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus