A fractional-order chaotic Lorenz-based chemical system: Dynamic investigation, complexity analysis, chaos synchronization and its application to secure communication

Abstract Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields, including cryptography, optics, and secure communications. In this paper, a three-dimensional fractional-order chaotic Lorenz model of chemical reactions is discussed. Some basic dynamical properties, such as stability of equilibria, Lyapunov exponents, bifurcation diagrams, Poincaré map, and sensitivity to initial conditions, are studied. By adopting the ADM algorithm, the numerical solution of the fractional-order system is obtained. It is found that the lowest derivative order in which the proposed system exhibits chaos is $q=0.694$ by applying ADM. The result has been validated by the existence of one positive Lyapunov exponent and by employing some phase diagrams. In addition, the richer dynamics of the system are confirmed by using powerful tools in nonlinear dynamic analysis, such as the 0-1 test and $C_{0}$ complexity. Moreover, modified projective synchronization has been implemented based on the stability theory of fractional-order systems. This paper presents the application of modified projective synchronization in secure communication, where the information signal can be transmitted and recovered successfully through the channel. MATLAB simulations are provided to show the validity of the constructed secure communication scheme.