Control over Slow Neuron Dynamics in the Stankevich-Mosekilde Model

Borisenok S.

1st International Conference on Innovative Academic Studies, Konya, Turkey, 10 - 13 September 2022, pp.645-648

  • Publication Type: Conference Paper / Full Text
  • City: Konya
  • Country: Turkey
  • Page Numbers: pp.645-648
  • Abdullah Gül University Affiliated: Yes


The family of so-called ‘Sherman models’ for biological neurons covers the dynamical nonlinear system with three variables: one for the action potential in the axon, one for the opening probability for the potassium channel in the cell membrane, and the third one for the slow probability of the channel evolution. Such an approach allows for describing the intermittency in the system dynamics due to the entering and leaving of the basins of different attractors. We discuss here the particular case of the Sherman model, the Stankevich-Mosekilde (SM) system, equipped additionally with the external control parameter. This external signal (in the form of an electrical current or an optogenetic simulation) drives the action potential variable which, in its turn, tracks the behavior of the slow membrane variable. The efficient tracking can be performed via the application of a few alternative algorithms: speed gradient or target attractor feedback. We demonstrate the principal possibility of the control over the slow dynamics in the system of SM ordinary differential equations and then we discuss how such control can be used for switching the dynamical regime among different attractors to model the processes of the hyper-synchronization in the small clusters of SM neurons to detect and suppress the epileptiform phase in the neural population. That can open a new gate for creating the theory of micro-epilepsy and serve as a theoretical base for developing AI expert systems.

Keywords – Sherman model for neurons, Slow variable dynamics, Feedback control, Speed gradient method, Epilepsy