Functions and Analysis


Nonlinear Dynamics in Signals Derived from Bessel Functions

Authors: Sai Venkatesh Balasubramanian

The present work purports to the formulation and characterization of signal based chaos based on Bessel Functions. Specifically, the variable in these functions is viewed as an additively coupled sum of sinusoidal signals, with competing frequencies. By adapting the regular and modified Bessel Functions of the first and second kinds 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 the regular and modified Bessel functions of the first kind exhibit rich, ornamental patterns, characteristic of quasiperiodicity and chaos. Using these, the bifurcation diagrams are plotted, and the chaotic behavior is quantitatively characterized using largest Lyapunov Exponents. It is seen that the nature of chaos in the generated 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] 2015-10-23 09:16:29

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