In this thesis, we introduce and analyze some new hyperchaotic complex nonlinear models with real and complex parameters. The dynamics of these models are rich in the sense that our models exhibit hyperchaotic attractors as well as chaotic, periodic, quasi-periodic and fixed points so- lutions. Also, we study the control and synchronizations of these new models.We study the effect of a complex flux-controlled memristor on a chaotic model to transform it to a hyperchaotic model. We are interested in ex- ploring the systems of the memristive because they are based on many applications in our lives such as including memory, computers, artificial intelligence and so on.The principal target of this work is to introduce and examine a novel kind of complex synchronization. This type called ”complex function projec- tive lag synchronization” (CFPLS).The results of this thesis are consistent with the Kingdom’s vision (2030), especially on cybersecurity, given the recent increase in cyber attacks. Various types of synchronization have been applied to secure communi- cations, and this supports our goals and aspirations to provide a secure communication and ensure the confidentiality of information transfer.