Combination synchronization of three classic chaotic systems using active backstepping design

Abstract

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis AIP Advances 6, 085121 (2016); 10.1063/1.4960110 Circuit simulation and physical implementation for a memristor-based colpitts oscillator AIP Advances 7, 035118 (2017);

Combination synchronization of hyperchaotic complex systems a vector norm based approach

“…In real life applications like secured communication, this reduces considerably the flexibility and the desired complexity of the synchronization system. Hence, new configurations are appeared, including three or four chaotic systems and referred, respectively, as combination synchronization [20], [21] or combination-combination synchronization [22], [23]. In the same trend, many recent works investigated combination synchronization among chaotic or hyperchaotic systems involving complex variables.…”

Compound-combination synchronization of chaos in identical and different orders chaotic systems

“…In 2011 and 2012, two papers were published on combination synchronization scheme for three chaotic systems [40,41]. These authors were the first to show the possibility of synchronizing the sum of the state variables of two drive systems with the state variables of a response system.…”

Generalized compound synchronization of chaos in different orders chaotic Josephson junctions

“…Recently, combination synchronization which involves two drive systems and one response system was investigated [22,23]. Also, combination-combination synchronization, where synchronization is achieved between two drive systems and two response systems was implemented, [24,25].…”

“…Synchronization and control of coupled chaotic systems have been widely investigated due to their potential applications in many fields such as neural networks, biological networks, secure communication etc. As a result of the diversity and complexity of dynamical behaviours of real complex systems, many kinds of synchronization types and schemes have been developed and investigated, such as complete synchronization [14], anti-synchronization [15], hybrid synchronization [16], projective synchronization [17], projective hybrid synchronization [18], reducedorder synchronization [19], increased order synchronization [20], function projective synchronization [21] combination synchronization [22,23], combination-combination synchronization [24,25], Compound synchronization [26] and so on. Meanwhile, many chaos control and synchronization methods have been proposed to design proper controllers, including feedback control method, adaptive control, active control, open-plus-closed-loop, backstepping, sliding mode control etc [27][28][29][30][31][32].…”