In this study mathematical model order reduction is applied to a nonlinear model of a network of biophysically realistic heterogeneous neurons. The neuron model describes a pyramidal cell in the hippocampal CA3 area of the brain and includes a state-triggered jump condition. The network displays synchronized ﬁring of action potentials (spikes), a fundamental phenomenon of sensory information processing in the brain. Simulation of the system is computationally expensive, which limits network size and hence biological realism. We reduce the network using advanced variations of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method. The reduced models should reproduce the original spiking activity. We show that reduction methods with online adaptivity achieve the most accurate reduction results. Some of the reduced models consume less computational resources than the original, at the cost of changes in population activity of the tested network model.