The synchronization of general complex dynamical network via pinning control

Abstract

In this paper, the globally synchronization of the general complex network is investigated. Firstly, we discuss the synchronization problem of the linearly coupled and directed network under the pinning control, and make comparison with the previous work about the undirected network. Sufficient conditions are obtained to guarantee the realization of synchronization. Secondly, the synchronization problem of nonlinearly coupled and undirected network under the pinning control is studied, and a criteria of getting synchronization is given. Furthermore, we introduced the adaptive adjustment of the coupling strength in nonlinearly coupled network. At last, we give simulation examples to verify our theoretical results.

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

“…If γ = 0, then , it is not consistent with the hypothesis . Remark In , synchronization of chaos systems was discussed with time‐delayed feedback controller u = k 1 e ( t ) + k 2 e ( t − τ ). In , synchronization conditions of complex networks with time‐varying delayed were obtained, τ ( t ) is the time‐varying delayed satisfying that , and the authors have concentrated on studying the presetting time‐varying delayed function in numerical examples yet. Here, the controller u = k 1 e ( t ) + k 2 e ( t − h ( t )) is time‐varying delayed, and h ( t ) is adaptive function.…”

“…However, owing to complexity of its form, few authors discussed synchronization of chaos systems with the time‐varying delayed feedback controller. In , the authors investigated synchronization of complex networks with time‐varying delayed. Note that the previous methods in are to obtain synchronization conditions for the time‐varying delay τ ( t ) satisfying that and , where are constants, and most of research efforts mentioned above have concentrated on studying the presetting time‐varying delayed function in numerical examples.…”

“…In , the authors investigated synchronization of complex networks with time‐varying delayed. Note that the previous methods in are to obtain synchronization conditions for the time‐varying delay τ ( t ) satisfying that and , where are constants, and most of research efforts mentioned above have concentrated on studying the presetting time‐varying delayed function in numerical examples. In addition, the economic chaotic systems are inevitably influenced by external disturbances stemmed from environmental interference, external disturbances may lead to the undesirable results of economic and financial chaotic systems, it is necessary to study the global stabilization of economic and financial chaotic systems with external disturbance, some results have been reported about stabilization of chaos systems under the presence of external disturbance .…”

“…However, owing to complexity of its form, few authors discussed synchronization of chaos systems with the time-varying delayed feedback controller. In [22][23][24][25], the authors investigated synchronization of complex networks with time-varying delayed. Note that the previous methods in [22][23][24][25] are to obtain synchronization conditions for the time-varying delay .t/ satisfying that 0 < .t/ Ä N and P .t/ Ä _ < 1, where N , _ are constants, and most of research efforts mentioned above have concentrated on influenced by external disturbances stemmed from environmental interference, external disturbances may lead to the undesirable results of economic and financial chaotic systems, it is necessary to study the global stabilization of economic and financial chaotic systems with external disturbance, some results have been reported about stabilization of chaos systems under the presence of external disturbance [26][27][28].…”

Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control

“…Various control schemes have been used to study the synchronization problems, and typical control methods include pinning control [7][8][9], adaptive control [10,11] and impulsive control [12][13][14][15][16]. Especially, impulsive control has captured a lot of researchers' attentions because of its applications in many areas such as orbital transfer of satellite, ecosystems management and chaos synchronization for secure communication.…”