Bogdanov-Takens singularity in a network of two coupled neurons with delayed feedbacks
A retarded functional differential equation with multiple discrete delays representing a network of two coupled neurons with delayed feedback is studied. By regarding the connection weights as the bifurcation parameters and analyzing the spectrum of the infinitesimal generator of the strongly continuous semigroup generated by the flows of the linearized system of the original system at the zero equilibrium, the phenomenon that the system under consideration can exhibit a Bogdanov-Takens bifurcation at the origin when the connection weights take a certain critical value. Based on the center manifold reduction and the normal form method for retarded functional differential equations, the second order normal form on the center manifold is obtained.
scientific article; zbMATH DE number 5620594