A new hyper-chaotic system and its synchronization

Universal Function Projective Synchronization of Chaotic Systems with Uncertainty by Using Active Fuzzy Sliding Mode Control

“…Here the UFPS of hyperchaotic Chen system (drive system) [27] and hyperchaotic Liu system introduced in [28] (response system) in the sense of hyperchaotic ChenLee system [29] (reference system) is considered by using the prescribed active fuzzy sliding mode control method. The drive, response and reference systems are respectively given by Uncertainties will be considered in the three system dynamics in matrices of form: Let us assume the uncertain nonlinear parts as…”

Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller

“…where V 1 (t) is the positive Lyapunov function defined in (9). The constant K 2 is positive, and it will be determined later.…”

“…In the previous two decades, control of chaotic synchronization has increasingly gained interests since the pioneering works of Pecora and Carroll [2] and Ott et al [3]. Until now, many advanced theories and methodologies have been developed for controlling chaotic synchronization of some types of chaotic/hyperchaotic attractors such as nonlinear active control methods [4][5][6][7][8][9], adaptive synchronization methods [10][11][12][13][14], backstepping design methods [15][16][17][18], and sliding mode control methods [19][20][21][22], and so on. However, due to the cross product terms of error states being involved in these control laws to cancel out the nonlinear parts of error dynamical systems, most aforementioned methods may be too complex to be implemented.…”

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

“…Different synchronization schemes for chaotic systems were studied and investigated [6][7][8][9][10]. Among these schemes, hybrid synchronization [11][12][13][14][15][16][17][18][19] is one in which some of the chaotic systems are synchronized whereas others are antisynchronized. Due to its importance, hybrid synchronization has been the subject of many research works.…”

“…Due to its importance, hybrid synchronization has been the subject of many research works. These works include study of synchronization/antisynchronization for permanent magnet synchronous motors connected in ring topology [11], function projective type synchronization for complex dynamical networks [12], investigation of complete synchronization and antiphase synchronization together [13], hybrid synchronization of networks having heterogeneous systems [14], study of synchronization for fractional-order systems [15], investigation of synchronization for systems with hyperchaotic nature [16,17], and study of synchronization for complex networks [18,19]. Study of hybrid synchronization involves multiple chaotic systems like complete, adaptive, global, projective, and antisynchronization systems [17,[20][21][22][23][24][25][26][27], and synchronization systems in multiple coupled complex networks [28,29].…”