Electrical Coupled Morris-Lecar Neurons: from Design to Pattern Analysis

Stéphane Binczak (1) , Rachid Behdad (1) , Vladimir I. Nekorkin (2) , Aleksei S. Dmitrichev (2) , M Rosse, (1) , Jean-Marie Bilbault (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]
2 Institute of Applied Physics of RAS

In this study, an experimental electronic neuron based on Morris-Lecar model is presented, able to become an experimental unit tool to study collective association of robust coupled neurons. The circuit design is given according to the ionic currents of this model. A weak coupling of such neurons under Multisim Software can generate clusters based on the boundary conditions of the neurons and their initial conditions. For this study, we work in the region close to the fold bifurcation of limit cycles. In this region two limit cycles exist, one of the cycles is stable and another one is unstable.

Mots clés: Cluster; Morris-Lecar; electrical neuron; fold bifurcation of limit cycles; OTA; Model; Bifurcations

Domaines: Mathématiques [math]; Physique [physics]

Stéphane Binczak, Rachid Behdad, Vladimir I. Nekorkin, Aleksei S. Dmitrichev, M Rosse,, et al.. Electrical Coupled Morris-Lecar Neurons: from Design to Pattern Analysis. International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), American Institute of Physics, Sep 2015, Rhodes, Greece. pp.210002, ⟨10.1063/1.4951985⟩. ⟨hal-01436605⟩