Complex Modified Projective Synchronization of Fractional-Order Chaotic Complex Systems

Shutang Liu (), Ping Liu (), Cuimei Jiang () and Changan Liu ()
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Shutang Liu: Shandong University, School of Control Science and Engineering
Ping Liu: Shandong Agricultural University
Cuimei Jiang: Qilu University of Technology (Shandong Academy of Sciences)
Changan Liu: Shandong University

Chapter 14 in Chaos in Complex Dynamical System: Theory and Application, 2026, pp 235-251 from Springer

Abstract: Abstract Complex modified projective synchronization (CMPS) is a new type of complex synchronization based on complex chaotic systems that was proposed almost simultaneously in 2013 [163, 164]. CMPS means that state variables of the master system converge to state variables of the slave system with a complex constant scaling matrix [224, 225]. In this chapter, we first investigates CMPS of the commensurate fractional-order chaotic complex systems by combining stability results of the fractional-order systems and the pole placement method. Subsequently,CMPS of fractional-order chaotic complex systems with incommensurate orders is investigated based on the stability theory of incommensurate fractional-order systems and active control method.

Date: 2026
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DOI: 10.1007/978-981-95-7762-0_14

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