Clown face in 3D chaotic system integrated with memristor electronics, DNA encryption and fractional calculus

This paper presents a three-dimensional sinusoidal forcing memristor-based chaotic model with one of its phase portrait trajectories visualized as a face or clown face. The developed novel chaotic model stability and its nature are analyzed using mathematical tools under the lights of Lyapunov exponents, maximal Lyapunov, Routh–Hurwitz criterion, and eigenvalues. The chaotic dynamics and richness of the pattern formation of novel coupled differential equations were numerically explored using different schemes, namely Caputo, Caputo–Fabrizio, and Atangana–Baleanu Caputo fractional derivatives. The electronic realization of the developed memristive-based model is presented with operational amplifiers and other passive electronic components, showing significant agreement with the numerical solution. The 3D system was chaotic, and its generated random numbers were tested with 0–1 chaos and NIST Suit tests. The randomness of the generated data is utilized to do DNA encryption as a method of encrypting data, with two dissimilar keys to scramble the image. The outcomes of the novel encryption method are demonstrated in three different ways (Pepper I, II, and III) and tested with standard image statistical tools.

Graphical abstract