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This article focuses on the problem of adaptive event-triggered anti-synchronization control for bidirectional associative memory neural networks subject to energy-limited denial of service attacks. First, a novel adaptive event-triggered scheme is developed by resorting to the acknowledgment character technique, which can help conserve valuable communication resources and has better performance in resisting malicious cyber attacks compared to traditional schemes. Second, a more general attack strategy for denial of service attacks is proposed with the consideration of energy constraints, and an anti-synchronization error system is established to analyze the anti-synchronization behavior. Then, sufficient conditions are provided to guarantee the anti-synchronization of drive and response bidirectional associative memory neural networks in H ∞ sense. Next, a design approach is obtained based on the above conditions for the controller gains. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed method and its superiority over the traditional event-triggered scheme. [ABSTRACT FROM AUTHOR]