Abstract
This paper's main objective is to reflect on hyperchaotic complex nonlinear systems' phase synchronization (PS) and anti-phase synchronization (APS). In these complex systems, the number of state variables can be expanded by isolating the real and imaginative parts. In PS, while their amplitudes stay uncorrelated, the position between two coupled chaotic (or hyperchaotic) systems remains in step with each other. The absence of the sum of relevant variables can characterize APS. To study PS and APS with complex variables of hyperchaotic nonlinear systems, the active control technique on the basis of stability analysis is proposed. PS and APS investigations for high dimensional systems are demonstrated by studying a 6-dimensional Di system. Phase synchronization concerns were also used to construct a straightforward and simple secure communication application. Numerical influences outlined for clarifying the phase synchronization of the hyperchaotic Lu model and for examining the gravity of scientific articulations' control powers.