Numerical Sensitivity Analysis and Hardware Verification of a Transiently-Chaotic Attractor

Author:

Sayed Wafaa S.1,Mohamed Sara M.2,Elwakil Ahmed S.3,Said Lobna A.2ORCID,Radwan Ahmed G.14

Affiliation:

1. Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt

2. Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza 12588, Egypt

3. Electrical and Computer Engineering, University of Sharjah, Sharjah 27272, United Arab Emirates

4. School of Engineering and Applied Sciences, Nile University, Giza 12588, Egypt

Abstract

We introduce a new chaotic system with nonhyperbolic equilibrium and study its sensitivity to different numerical integration techniques prior to implementing it on an FPGA. We show that the discretization method used in numerically integrating the set of differential equations in MATLAB and Mathematica does not yield chaotic behavior except when a low accuracy Euler method is used. More accurate higher-order numerical algorithms (such as midpoint and fourth-order Runge–Kutta) result in divergence in both MATLAB and Mathematica (but not Python), which agrees with the divergence observed in an analog circuit implementation of the system. However, a fixed-point digital FPGA implementation confirms the chaotic behavior of the system using Euler and fourth-order Runge–Kutta realizations. Therefore, the increased sensitivity of chaotic systems with nonhyperbolic equilibrium should be carefully considered for reproducibility.

Funder

Science, Technology, and Innovation Funding Authority

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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