| Summary: | A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system. Keywords: Chaotic, Control, Synchronization, Lyapunov stability, Complex
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