Functions and Analysis


Generating Chaos from Love - Mathematically

Authors: Sai Venkatesh Balasubramanian

The present paper pertains to the formulation and generation of a signal based frequency controlled chaos based on the Heart Curves, an assortment of parametric functions so named due to their ability to generate cardoid (heart-shaped) curves. Specifically, the variable in two parametric functions is taken as an additively coupled sum of sinusoids with competing frequencies. By adapting the x and y components of these functions into signals, the time derivatives are computed and used to form the iterative maps and phase portraits. It is seen that the four phase portraits display to varying degrees, ornamental patterns, characteristic of quasiperiodicity and chaos. Using these, bifurcation diagrams are plotted in order to investigate the chaotic behavior. It is seen that the nature of chaos in the generated signals 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, forming the novelty of the present work.

Comments: 6 Pages.

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Submission history

[v1] 2015-10-26 08:34:31

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