Several neurodegenerative diseases impact the olfactory system, and in particular the olfactory bulb, early in disease progression. One mechanism by which damage occurs is via synaptic dysfunction. Here, we implement a computational model of the olfactory bulb and investigate the effect of weakened connection weights on network oscillatory behavior. Olfactory bulb network activity can be modeled by a system of equations that describes a set of coupled nonlinear oscillators. In this modeling framework, we propagate damage to synaptic weights using several strategies, varying from localized to global. Damage propagated in a dispersed or spreading manner leads to greater oscillatory power at moderate levels of damage. This increase arises from a higher average level of mitral cell activity due to a shift in the balance between excitation and inhibition. That this shift leads to greater oscillations depends critically on the nonlinearity of the activation function. Linearized analysis of the network dynamics predicts when this shift leads to loss of oscillatory activity. We thus demonstrate one potential mechanism involved in the increased gamma oscillations seen in some animal models of Alzheimer's disease, and we highlight the potential that pathological olfactory bulb behavior presents as an early biomarker of disease.