Hybrid Projective Synchronization of Fractional Order Chaotic Complex Nonlinear Systems With Time Delays

Abstract

Time delays are frequently appearing in many reallife phenomena and the presence of time delays in chaotic systems enriches its complexities. The analysis of fractionalorder chaotic real nonlinear systems with time delays has a plenty of interesting results but the research on fractionalorder chaotic complex nonlinear systems with time delays is in the primary stage. This paper studies the problem of hybrid projective synchronization (HPS) of fractionalorder chaotic complex nonlinear systems with time delays. HPS is one of the extensions of projective synchronization, in which different state vectors can be synchronized up to different scaling factors. Based on Laplace transformation and the stability theory of linear fractionalorder systems, a suitable nonlinear controller is designed to achieve synchronization between the master and slave fractionalorder chaotic complex nonlinear systems with time delays in the sense of HPS with different scaling factors. Finally, the HPS between fractionalorder delayed complex Lorenz system and fractionalorder delayed complex Chen system and that of fractionalorder delayed complex Lorenz system and fractionalorder delayed complex Lu system are taken into account to demonstrate the effectiveness and feasibility of the proposed HPS techniques in the numerical example section.