An exponential jerk system, its fractional-order form with dynamical analysis and engineering application

Abstract

A simple jerk system with only one exponential nonlinearity is proposed and discussed. Dynamic analysis of the integer-order jerk system shows the existence of chaotic oscillations. A model for the fractional-order jerk system is derived. The Adomian decomposition method is used to analyse the fractional-order jerk system. Stability analysis of the fractional-order jerk system shows that chaotic oscillations exist in orders less than one and bifurcation analysis shows the range of fractional orders for periodic and chaotic oscillations. To show the randomness of the fractional-order jerk system, a pseudorandom number generator is designed and tested. The NIST-800-22 tests show that the proposed fractional-order jerk system is effective in showing randomness. Finally, an image hiding application to the audio data has been realized by using the developed RNG algorithm. The encrypted image is hidden by being embedded in the audio data, and then, on the receiver side, the data are recovered by taking the image data from the hidden audio file.