Dynamical analysis and encryption key-distribution application of new q-deformed reduced Lorenz system

• Published in: SeMA journal Vol. 80; no. 1; pp. 131 - 158
• Main Authors: Elsonbaty, A., Salman, Sanaa M., Aldurayhim, A., Abdo, N. F., Hagras, E. A., Elsadany, A. A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-03-2023; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Bifurcations; Deformation effects; Dynamical systems; Liapunov exponents; Lorenz system; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear dynamics; Parameters; Stability analysis; System dynamics; 34C05; Image encryption; 39A30; q-Deformed map; Key-distribution; 93D15; Codimension-one bifurcation; Reduced Lorenz system; Local stability; 39A50
• ISSN: 2254-3902; 2281-7875
• DOI: 10.1007/s40324-021-00271-0

The aim of this work is to analytically investigate the nonlinear dynamic behaviors of a proposed reduced Lorenz system based on q-deformations. The effects of varying the new q-deformation parameter on the dynamical behaviors of the system along with the induced bifurcations of fixed points are explored. In particular, the codimension-one bifurcation analysis is carried out at interior fixed point of the q-deformed system. Explicit conditions for the existence of pitchfork and Neimark–Sacker bifurcations are obtained. Numerical simulations are performed to confirm stability and bifurcation analysis in addition to investigate the effects of variations in system parameters. The changes in system dynamics are explored via the bifurcation diagrams, phase portraits and time series diagrams. Moreover, the quantification of system complex behaviors is depicted through the maximal Lyapunov exponent plots. A cascaded version of the model is proposed to boost its complex dynamics. Then, a chaos-based image encryption scheme, relying on a proposed key-distribution algorithm, is introduced as an application. Finally, several aspects of security analysis are examined for the encryption system to prove its efficiency and reliability against possible attacks.