Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
The authors study a unidirectional ring of three scalar cells which are coupled by a distributed delay: \[ x_{j+1}(t) = -x_{j+1}(t) + c_j\tanh \left[ \int_{-\infty}^{t}\kappa(t-s)x_j(s)ds\right],\;j=1,2,3, \] where the delay kernel is given by \(\kappa(s) = \beta e^{-\beta s}\). They give sufficient conditions for the stability of equilibria and determine critical parameter values for Hopf bifurcations. They use the method of multiple scales to determine direction and stability of the Hopf bifurcations and show that there exists a global Hopf bifurcation.
scientific article; zbMATH DE number 6122177
scientific article