Normal neural population activity and information encoding in the hippocampus can be modeled with ring attractors dynamics[1], but this representation has not yet been linked to pathological hippocampus activity such as temporal lobe epileptic seizures. In this study, we wanted to investigate under which conditions these dynamic models can develop oscillatory activities characteristic of the temporal lobe epilepsy. In particular, we focused on the influence of the synaptic connectivity[2][3]. We performed the analysis of networks consisting in one or two rings of excitatory or inhibitory rate model neurons with piece-wise linear activation functions and spatially symmetric synaptic connections. We evaluated their stability under constant input current considering either the role of the real/complex eigenvalues of the system or the role of the switches dues to the nonlinearity of its activation functions. Our main results are that : (1) single-ring networks cannot oscillate, neither due to their eigenvalues nor due the nonlinearity of their activation functions, and (2) two-ring networks have more complex dynamics that enable them to exhibit either normal or pathological activity, depending on their connectivity. In particular, switches proveoked by the nonllinear activation functions can cause these systems to present a limit cycle. We then verified our predictions using network simulations, for different synaptic connection range and different input levels. In the case of two-ring networks, we observed that networks with only short-range synaptic connections were stable for all inputs, thus describing healthy hippocampus activity, whereas networks with unbalanced connections could oscillate for certain input levels, while remaining stable for others, thus representing plausible epileptic networks.