2000/01/01 by Leslie P. Shayer, Sue Ann Campbell · 5 citations
Computer Science · Physics and Astronomy · #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · doi:10.1137/s0036139998344015
crossref issued 2000/01/01 · crossref published 2000/01/01 · crossref published-print 2000/01/01 · openalex publication_date 2000/01/01 · crossref created 2003/06/11 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01 · crossref indexed 2026/08/01
A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. It is shown that the trivial fixed point may lose stability via a pitchfork bifurcation, a Hopf bifurcation, or one of three types of codimension-two bifurcations. Multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations.