Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model

Abstract

Mixed-mode oscillations (MMOs) and canards play important role in the dynamics of many mathematical models in the life sciences. In particular, pathological early afterdepolarizations in heart cells behavior can be associated with MMOs. The present paper aims to study a stochastic version of the reduced Luo–Rudy model of cardiac action potential. We show that in the parameter zone where the dynamics of the original deterministic system is characterized by canard-type limit cycles, weak additive noise can induce MMOs. Using stochastic sensitivity functions, Mahalanobis metrics, and confidence domains, we analyze the probabilistic mechanism of this stochastic phenomenon. Moreover, we find a critical value of the parameter corresponding to the “super-sensitive” cycle and show that for this value, stochastic splitting of oscillations is observed. Furthermore, we show that in the canard zone of the model, noise-driven transition to chaos occurs. To conclude, this paper reveals and analyzes new stochastic phenomena in the model of cardiac activity, moreover, the presented results can be helpful for studies of other complex models.