Abstract
Our primary goal of this work is to exhibit and examine a novel kind of complex synchronization. We may call it a complex phase synchronization (CPHS). There are bizarre properties of the CPHS and do not exist in the writing, for example, (i) this sort of synchronization can be investigated just for complex nonlinear systems; (ii) the CPHS contains or includes two sorts of synchronizations (anti-phase synchronization APS and phase synchronization PHS); (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A description of the CPHS is presented for two identical chaotic or hyperchaotic complex nonlinear models. In view of the stability theorem, a scheme is intended to fulfill CPHS of chaotic or hyperchaotic attractors of these systems. The effectiveness of the acquired outcomes is shown by a reproduction illustration on the hyperchaotic complex Chen system. Numerical outcomes are plotted to show state variables, modulus errors, phase errors and the development of the attractors of these hyperchaotic models after synchronization to demonstrate that CPHS is achieved.