<p>In this paper, the synchronisation problem of quaternion-valued Takagi-Sugeno fuzzy neural networks with time-varying delays is discussed based on the event-triggered mechanism. To avoid frequent switching and oscillation of the signal, the exponential gain method is fully utilised. The main novelty of the method is the introduction of an exponential term which makes the control gain variable over two consecutive event time intervals. Thus, based on this exponential gain method, a fuzzy exponential gain event-triggered controller is designed, as well as a suitable Lyapunov function is constructed to obtain the synchronisation condition under static event-triggered. Since the newly designed controller no longer contains sign functions, jittering is also avoided. In addition, in order to reduce the number of triggers more efficiently, the concept of dynamic event-triggered conditions is introduced, with the consequent provision of a sufficient basis for judgement. At the same time, through rigorous mathematical derivation, the lower bound of the time interval is proved to be greater than zero, thus effectively ruling out the possibility of Zeno’s phenomenon. Finally, the validity and feasibility of the theoretical analyses are demonstrated by numerical arithmetic examples.</p>