Comprehensive analysis of slow-fast denatured Morris-Lecar neurons

Neurons represent the fundamental units of the nervous system, and modeling their dynamics as slow-fast systems is becoming increasingly ubiquitous in the neurodynamics literature. We look into slow-fast denatured Morris-Lecar neurons, both single and coupled systems, aimed at capturing their bursting patterns. We employ a range of tools from nonlinear dynamics to analyze the single and coupled systems, for example, fixed point analysis and bifurcation analysis. We perform numerical simulations exhibiting a route consisting of hyperchaos, chaos, quasiperiodicity, mixed-mode oscillations, irregular bursting, and decay oscillations. Chaos is studied via numerical computations of Lyapunov exponents and also employing the 0-1 test. Furthermore, the complexity of the time series arising from the coupled system is quantified via sample entropy. Finally, the synchronization between the neurons in the coupled system is studied using the cross-correlation coefficient and whether it contributes to the complexity of our model is identified numerically. We observe in-phase and antiphase synchrony between the two neurons in the coupled system and notice that antiphase synchrony contributes towards more complexity within the system.