This paper addresses a novel prescribed performance synchronization of complex dynamical networks by means of event-triggered communication protocols.With the designed controller and proposed even-triggered communication strategy, this paper have advantages of guaranteeing the transient and steady-state performance of complex dynamic networks and avoiding the continuous communication of networks for reducing the number of communications and saving the network resources. In addition, the Zeno behavior is avoided in the networks. At last, the effectiveness of the theoretic results obtained is verified via the application in the complex dynamical network with Chua's circuit.As we all know, in the past several years, with the rapid development of digital computers, the event-based communication schemes have received significant attention in signal processing. 24,25 Considering the event-based communication schemes, the information transmission from the sensors to the networks is permitted only when a particular condition of the event trigger function holds. Therefore, different from the common continuous transmission of information, the event-based communication mechanism can reduce the waste of network resources. To the present, the event-based communication synchronization problems of CNs have yielded considerable results. [26][27][28] Concretely, in the work of Li et al, 29 the authors studied the event-triggered intermittent communication synchronization problems for general directed CNs, which proposed a unified framework for synchronization and designed a newfangled distributed event-triggering sampling control method. For the Markovian jump CDNs with delayed, in the work of Zhou et al, 30 the researchers studied the exponential synchronization problems by proposing a novel randomly occurring event-based control method. The synchronization problems of CNs were investigated in the work of Dai et al 31 via distributed event-triggered communication method. Although the literary works mentioned earlier have contributed to the synchronization problem of event-driven communication in complex dynamic networks, the significance of the transient problem of synchronization course has not been considered.In fact, the transient performance of synchronization process is an important factor to consider. [32][33][34] In traditional synchronization course of CNs, the synchronization errors are testified to converge within a bounded set near zero, whose size decides by the designed parameters and some unknown bounded terms. Then, the prescribed performance control method 32 is raised to ensure that the tracking errors gather to a predefined bound accompanying with the convergence rate no less than a certain value. So far, the prescribed performance issues 32 have been expanded to the multiagent systems 35 and the complex dynamical (networks) systems. 36 However, the results proposed in related works 32-37 do not consider the event-triggered communication problem. As far as our knowledge is concerned, up to the present, no resul...