A novel sort of adaptive complex synchronizations of two indistinguishable chaotic complex nonlinear models with uncertain parameters and its applications in secure communications

In this paper, we will demonstrate the adaptive complex anti-lag synchronization (CALS) of two indistinguishable complex chaotic nonlinear systems with the parameters which are uncertain. The significance of CALS is not advised well in the literature yet. The CALS contains or consolidate two sorts of synchronizations (anti-lag synchronization ALS and lag synchronization LS). The state variable of the master system synchronizes with an alternate state variable of the slave system. Depending on the function of Lyapunov, a plan is orchestrated to achieve CALS of chaotic attractors of complex systems with unverifiable parameters. CALS of two indistinguishable complexes of Lü systems is viewed as, for example, an occasion for affirming the likelihood of the plan exhibited. In physics, we can see complex chaotic systems in numerous different applications, for example, applied sciences or engineering. With a specific end goal to affirm the proposed synchronization plan viability and demonstrate the hypothetical outcomes, we can compute the numerical simulation.The above outcomes will give the hypothetical establishment to the secure communication applications. CALS of complex chaotic systems in which a state variable of the master system synchronizes with an alternate state variable of the slave system is an encouraging sort of synchronization as it contributes excellent security in secure communication. Amid this secure communication, the synchronization between transmitter and collector is shut and message signals are recouped. The encryption and restoration of the signals are simulated numerically. Keywords: Complex anti-lag synchronization, Chaotic system, Synchronization, Uncertain, Error function, Lyapunov function, Complex