Stumped nature hyperjerk system with fractional order and exponential nonlinearity: Analog simulation, bifurcation analysis and cryptographic applications

This article presents the construction and consumption of hyperjerk system having chaotic nature with the commensurate ordered fractional derivative on rapidly digitalized emerging technologies. The system analyzed analytically using Lipschitz condition and numerically with the help of predictor corrector approaches. Originality of constructed system is confirmed using log error plots which gives satisfactory small values on finite time scale. The dynamical performances of the complex system are termed in multiple phase planes by the mean of their significant nature. Stability and bifurcation analysis around the fractional derivative is also studies for the various parameter of system to check the visibility of chaotic solution. The system is also designed in analog circuit simulator with the aid of operational amplifier, anti-parallel semiconductor diodes for validation of the system. With the help of random number generators (RNGs), binary array generated from the hyperjerk system and plugged in to the NIST 800-22 test suite to measure the randomness. The array having high randomness is used as strong cypher key for the cryptographic execution straightforwardly in both direction encryption and decryption.

Automated summary

This article presents the construction and consumption of a hyperjerk system with chaotic nature, analyzing the system's dynamical performances, stability, and bifurcation analysis. The binary array generated from the system using random number generators is used as a strong cryptographic key for straightforward encryption and decryption in both directions.