Synchronization of impulsively coupled complex networks

Sun, Wen; Chen, Zhong; Chen, Shihua

doi:10.1088/1674-1056/21/5/050509

Cited by 7 publications

(4 citation statements)

References 28 publications

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“…[5][6][7][8] CS means the complete coincidence of the states of all oscillators no matter what the states will be, which appears only if the interacting oscillators are identical. [9][10][11] If the oscillators cannot achieve CS by themselves, various approaches such as linear feedback control, [12][13][14][15] adaptive control, [16][17][18][19] pinning control, [20][21][22][23] time-triggered impulsive control, [24][25][26] event-triggered impulsive control, [27,28] and sampled control [29] have been put forward to guide all the oscillators to reach the desired goal. AD refers to a coupling-induced suppression of oscillating by stabilizing an existing homogeneous steady state.…”

Section: Introductionmentioning

confidence: 99%

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points*

Sun¹,

Li²,

Guo³

et al. 2021

Chinese Phys. B

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The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic, and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling, death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented.

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Section: Introductionmentioning

confidence: 99%

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points*

Sun¹,

Li²,

Guo³

et al. 2021

Chinese Phys. B

Self Cite

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“…The study of synchronization among oscillators has a long history. [1][2][3][4][5][6][7] In most works, the effect of oscillators on each other has been assumed to be rapid and without delay, which is an ideal assumption. However, we know that the mutual interaction of oscillators in nature occurs with some delays.…”

Section: Introductionmentioning

confidence: 99%

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

2013

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In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

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“…Synchronization of complex dynamical networks has received a great deal of attention from the systems science community in the last decade. [4][5][6][7][8][9][10][11][12][13][14][15] Using the master stability function, [4] Pecora and Carroll developed a general approach to the synchronization of identical dynamical systems. They discovered a bounded synchronization region for the coupling chaotic systems, and showed that if the coupling strength is greater than a threshold, the coupling chaotic systems cannot achieve synchronization.…”

Section: Introductionmentioning

confidence: 99%

Explosive synchronization of complex networks with different chaotic oscillators

Zhao¹

2013

Chinese Phys. B

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Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Gómez-Gardeñes J, Gómez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldú J M, Sendiña-Nadal I, Gómez-Gardeñes J, Arenas A, Moreno Y, Gómez S, Jaimes-Reátegui R and Boccaletti S 2012 Phys. Rev. Lett. 108 168702]. Here, we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks. The continuous transition is discovered for Rössler systems in both of the above complex networks. However, explosive transitions take place for the coupled Lorenz systems, and the main reason is the abrupt change of dynamics before achieving complete synchronization. Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.

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Synchronization of impulsively coupled complex networks

Cited by 7 publications

References 28 publications

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points*

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points*

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

Explosive synchronization of complex networks with different chaotic oscillators

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