Abstract: The dynamics of a discrete and dissipative nonlinear model neuron is discussed. Numerical simulations demonstrate that the self-inhibitory units with non-zero decay rates exhibit a complex dynamics including period doubling routes to chaos. A BP/CNN hybrid neural network is constructed using the chaotic neuron in the neural network to conduct an after-processing for the output from BP network, with the reverse bifurcation of the chaotic neuron used to implement time-delay classification. The BP/CNN network thus constructed can detect the SYN flooding misuse intrusion featured with typical time-delay behavior. The result shows that these types of hybrid neural network have a capability for flexible time-delay classification so as to extend the computational capability of BP neural network and provide a new type of classifying method. The proposed neural network can be generalized to other time-delay classification.