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Simplified neuronal models capture the essence of the electrical activity ofa generic neuron, besides being more interesting from the computational pointof view when compared to higher dimensional models such as the Hodgkin-Huxleyone. In this work, we propose a generalized resonate-and-fire model describedby a generalized Langevin equation that takes into account memory effects andcolored noise. We perform a comprehensive numerical analysis to study thedynamics and the point process statistics of the proposed model, highlightinginteresting new features like: i) non-monotonic behavior (emergence of peakstructures, enhanced by the choice of colored noise characteristic time-scale)of the coefficient of variation (CV) as a function of memory characteristictime-scale, ii) colored noise-induced shift in the CV, and iii) emergence andsuppression of multimodality in the interspike interval (ISI) distribution dueto memory-induced subthreshold oscillations. Moreover, in the noise-inducedspike regime, we study how memory and colored noise affects the coherenceresonance (CR) phenomenon. We found that for sufficiently long memory, CR isnot only suppressed, but also the minimum of the CV $\times$ noise intensitycurve that characterizes the presence of CR may be replaced by a maximum. Theaforementioned features allow to interpret the interplay between memory andcolored noise as an effective control mechanism to neuronal variability. Sinceboth variability and non-trivial temporal patterns in the ISI distribution areubiquitous in biological cells, we hope the present model can be useful inmodeling real aspects of neurons.

Colored noise and memory effects on formal spiking neuron models