Abstract
Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. At present, many results of ES are based on the networked Kuramoto oscillators and little attention has been paid to the influence of chaotic dynamics on synchronization transitions. Here, the unified chaotic systems (Lorenz, Lü and Chen) and R?ssler systems are studied to report evidence of an explosive synchronization of chaotic systems with different topological network structures. The results show that ES is clearly observed in coupled Lorenz systems. However, the continuous transitions take place in the coupled Chen and Lü systems, even though a big shock exits during the synchronization process. In addition, the coupled R?ssler systems will keep synchronous once the entire network is completely synchronized, although the coupling strength is reduced. Finally, we give some explanations from the dynamical features of the unified chaotic systems and the periodic orbit of the R?ssler systems.
Highlights
Complex networks are ubiquitous in the world, such as transportation networks, Internet, wireless networks and phone networks
Motivated by the above discussions, this paper investigates explosive synchronization in complex dynamical networks coupled with chaotic systems
It may be possible that explosive synchronization emerges by imposing a positive correlation between the heterogeneity of the network structures and node dynamics, which is worthy of further investigation
Summary
Complex networks are ubiquitous in the world, such as transportation networks, Internet, wireless networks and phone networks. Zhao [12] studied explosive synchronization of complex networks with different chaotic oscillators and indicated that explosive synchronization only takes place in the coupled Lorenz systems. Explosive synchronization can be said to happen in complex networks when the following conditions are satisfied: 1) the emergence of the first-order transition and 2) the hysteresis curve appears in the process from synchrony to incoherence. Motivated by the above discussions, this paper investigates explosive synchronization in complex dynamical networks coupled with chaotic systems. The numerical simulations show that explosive synchronization is obviously discovered in the coupled Lorenz systems of different structures, but there are not obvious first-order transitions and hysteresis curves for coupled Lü and Chen systems.
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