Neuroscience

The entrainment of biological oscillators is a classic problem in the field of dynamical systems and synchronization. This paper explores a novel type of entrainment mechanism referred to as polyglot entrainment 1 (multiple disconnected 1:1 regions for a range of forcing amplitude) for higher dimensional nonlinear systems. Polyglot entrainment has been recently explored only in two-dimensional slow-fast models in the vicinity of Hopf bifurcations (HB). Heading towards generality, in this research, we investigate the phenomenon of polyglot entrainment in higher-dimensional conductancebased models including the four-dimensional Hodgkin-Huxley (HH) model and its reduced three-dimensional version. We utilize dynamical systems tools to uncover the mechanism of entrainment and geometric structure of the null surfaces to explore the conditions for the existence of polyglot entrainment in these models. In light of our findings, in the vicinity of HB, when an unforced system acts as a damped oscillator and the fixed point is located near a cubic-like manifold, polyglot entrainment is observed.

Resonance and synchronized rhythm are significant phenomena observed in dynamical systems in nature, particularly in biological contexts. These phenomena can either enhance or disrupt system functioning. Numerous examples illustrate the necessity for organs within the human body to maintain their rhythmic patterns for proper operation. For instance, in the brain, synchronized or desynchronized electrical activities can contribute to neurodegenerative conditions like Huntington’s disease. In this paper, we utilize the well-established Hodgkin–Huxley (HH) model, which describes the propagation of action potentials in neurons through conductance-based mechanisms. Employing a “data-driven” approach alongside the outputs of the HH model, we introduce an innovative technique termed “dynamic entrainment.” This technique leverages deep learning methodologies to dynamically sustain the system within its entrainment regime. Our findings show that the results of the dynamic entrainment technique match with the outputs of the mechanistic (HH) model.