A Brief Note on Recurrence Quantification Analysis of Bipolar Disorder Performed by Using a van der Pol Oscillator

Assuming a mathematical model based on van der Pol oscillator, we simulated the time course of the latent and acclaimed phases of the psychiatric pathology called bipolar disorder. Results were compatible with the analysis of experimental time series data of mood variation previously published by Gottschalk A. et al., (1995). Furthermore we performed Recurrence Quantification Analysis (RQA) of time series data generated by our mathematical model and we found that the obtained values for Recurrences, Determinism and Entropy may be considered as indexes of the increasing severity and stage of the pathology. We consequently suggest that these variables can be used to characterize the severity of the pathology in its observed stage. On the basis of the model, an attempt has also been made to discuss some aspects of the complex dynamics of the pathology. Results suggest that stochastic processes in mood variation of normal subjects play an important role to prevent mood from oscillating in a too rhythmically recurrent and deterministic way, as it occurs in bipolar disorder.