Modeling state transition of hippocampal local field potential between theta rhythm and large irregular amplitude activity by bifurcation between a limit cycle and chaotic dynamics

Here we propose a possible mathematical structure of the state transition of the hippocampal local field potential (LFP) between theta rhythm and large irregular amplitude activity (LIA) in terms of nonlinear dynamics. The basic idea is that the alternation of the state between theta rhythm and LIA can be interpreted as a bifurcation of the attractor between a limit cycle and chaotic dynamics. Tsuda et al. reported that a network composed of simple class 1 model neurons connected with gap junctions shows both synchronous periodic behavior and asynchronous chaotic behavior [1]. Here we model the network of hippocampal interneurons extending their model. The network is composed of electrically coupled simple 2-dimensional neurons with natural resonant frequency in the theta frequency. We incorporate a periodic external force representing the medial septal afferent. The system converges on a limit cycle under this external force, but shows chaotic dynamics without this external force. Furthermore, the external noise realized rapid alteration of the state obeying the change of the amplitude of the septal input.