Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

“…(17) and slave system (18) asymptotically synchronize, then the systems (19) and (20) which were derived from the change of space also asymptotically synchronize, such that…”

“…MPS means that the master and slave systems could be synchronized up to a constant scaling matrix. Recently, various control methods which include adaptive control [17,18] and active control [7,19,20] have been introduced. Most of the works done on MPS of chaotic systems have used active control method since it is easy to design a control input and to deal with equations including scaling functions.…”

Finite-time generalized synchronization of chaotic systems with different order

“…In order to depict the evolution situation of error states e 1 and e 2 , we choose β = 1/999, β = 1/19. Then the finite-time generalized synchronization error state trajectories between the systems (15) and (16) are shown in Fig. 2.…”

“…So, the study of synchronization for different order chaotic systems is very important to the perspective of control theory and practical application. Some theoretical results for the synchronization between different order chaotic systems have been obtained [12][13][14][15][16][17]. The synchronization is only attained by reduced order, because the order of the response system is lower than that of the drive system in [12][13][14][15].…”

“…The synchronization is only attained by reduced order, because the order of the response system is lower than that of the drive system in [12][13][14][15]. The reduced order and increased order modified full state hybrid projective synchronization are studied in [16]. An approach based on the Lyapunov stability theory is given to realize the generalized synchronization of different order chaotic systems in [7].…”