This study examines the application of Lyapunov exponent analysis (LE) to characterize local field potentials (LFPs) from hippocampal brain slices in animal models, with a focus on distinguishing between basal and active states of hippocampal activity. We used LFP recordings obtained from hippocampal slices treated with kainic acid to induce active states, capturing transitions and sustained periods of activity. The signals were pre-processed to standardize their length and filtered using a 4th-order Butterworth bandpass filter to isolate gamma oscillations. LE analysis was used to assess the dynamical behavior of these signals, revealing that positive LE values indicate chaotic dynamics, which were prevalent in the active state recordings. Further analysis using time-series clustering distinguished patterns in progression from the basal to active states, suggesting that LE could serve as a biomarker for neurophysiological and pathological conditions, including Alzheimer's disease. Our findings suggest that LE analysis provides a novel approach to understanding the complex dynamics of the hippocampus, potentially contributing to the early diagnosis of neurodegenerative diseases.