Qualitative study of the fractional order nonlinear chaotic model: electronic realization and secure data enhancement

In this work, we explore the superposition of two well-known chaotic oscillators, namely, the Duffing double-well and the forced van der Pol with the fractional order derivative. The proportional fractional derivative has been taken for numerical simulations and highly chaotic solution to improve some information of security systems has been found. The existence and the uniqueness of a super system are stated in the form of theorems using the Lipschitz condition locally. The qualitative properties of chaotic dynamics are described by mean of Lyapunov exponent (LE), eigenvalues, bifurcation and Poincare maps. The analog circuit is also intended, with the help of different physical instruments, to validate the superposition of chaotic systems. The randomness level of a superposition chaotic system is tested via standard test suite, and the qualified set of a 32-bit array with high haphazardness is used for encryption as well as decryption. Furthermore, a security analysis is performed using different parameters, such as the uncertainty, similarity etc. The outcomes for the properties, time evolution, phase portrait, and oscilloscopic views are presented in tabulated and graphical forms.

Automated summary

This work explores the superposition of two well-known chaotic oscillators, finding highly chaotic solutions through numerical simulations and proving the existence and uniqueness of a super system using the Lipschitz condition. The qualitative properties of chaotic dynamics are described using Lyapunov exponent, eigenvalues, bifurcation, and Poincare maps, with validation of the superposition of chaotic systems using analog circuit design. Testing the randomness level and security features of the superposition chaotic system are conducted, and outcomes are presented in tabulated and graphical forms.