Secure communications via modified complex phase synchronization of two hyperchaotic complex models with identical linear structure and adjusting in nonlinear terms

We present a novel modified complex phase synchronization (MCPS) focusing on two hyperchaotic complex systems, including a comparative structure of direct terms with absolutely differing or not completely in nonlinear terms. We have used the active control theory for analytical control limits to achieve MCPS. It is shown that MCPS contains two sorts of synchronizations (phase and anti-phase synchronizations) and the state variables of the master system synchronize with substitute state components of the slave system. Numerical results are portrayed out to reveal the phases and modules errors of these hyperchaotic complex attractors, where the complex systems appear in various basic fields of material science and building. Also, we found that MCPS of the hyperchaotic complex structure synchronizes with another state variable of the slave structure is an empowering sort of synchronization as it contributes fabulous security in secure communication. In this secure communication, synchronization amongst transmitter and collector is closed and message signals are recovered. The encryption and recovery of the signals are imitated numerically.