Bird-Like Trajectories in 6D Chaotic System Integrated with Fractional Order Derivative, Memristor, and Encryption

This paper reports a novel six-dimensional nonlinear dynamical system with the tangent hyperbolic memristor circuit and amalgamated image encryption. The dynamical system is analyzed using standard tools, including phase portraits, equilibrium points, Eigenvalues, and Lyapunov exponents. The analysis suggests that the developed system is chaotic in nature and has exciting new 2D trajectories. The system generates two different trajectories of bird-like phase portrait. The chaotic system is numerically solved with Caputo fractional order derivative for different values of fractional order (q). The fractional order circuits are designed for q = 1 and q = 0.99 utilizing the approximation fractional order technique of transfer function, showing a great deal of agreement with the numerical results. Lastly, the random number generated from the chaotic system is utilized to scramble the image via the scheme of Amalgamated Image Encryption. The scrambled image is tested using a different image security test algorithm to support the idea that the chaotic system and image can together form an advantageous key.