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In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance, dissipativity, equilibria and their stability, Lyapunov exponents and bifurcation diagram. Then adaptive modified function projective synchronization (MFPS) problem of chaotic complex systems with unknown parameters is studied. By Lyapunov stability theory, the adaptive control law and the parameters update law are derived to make the state of two chaotic complex systems modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.