An analysis of the entrainment of a thalamacortical neuron to periodic sensorimotor signals
Amanda Gayle Johnson, Yixin Guo, Dennis Guang Yang · 2025
The goal of this work is to analyze the thalamacortical neuron and the possible dynamics of its various states. We entrain the thalamacortical dynamical system to a periodic sensorimotor signal where the signal behaves as the switch to the system. We identify the behavior of the isochrons when the switch is on and employ Floquet theory to give an analytical description of the on-system, thereby reducing the dimensionality by one. This allows for a denser discretization of the system as a whole. Using the discretization, we can identify the bifurcating states of the system associated with good, bad, and miss responses to input stimuli where the bifurcating parameter is the time-length of the excitatory input. We then go on to consider the dynamics of the neuron for various fixed periodic signals. Wherein our goal is to fully understand the impetus responsible for observable system dynamics. In these observations we see the discrete behavior of various stability combinations including the emergence of homoclinic tangles. We come to understand the shift in behavior between parameter values as location, number, and type of fixed points vary.