2016/06/23 by Stephen Lynch, Jon Borresen, Lynch, Stephen +1
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #34C15 #34C55 #Adaptation and Self-Organizing Systems (nlin.AO) #Artificial intelligence #Bifurcation #Bifurcation diagram #Bifurcation theory #Biological applications of bifurcation theory #Bistability #Computer science #Control theory (sociology) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical analysis #Mathematics #Multistability #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Period-doubling bifurcation #Physics #Pitchfork bifurcation #Quasiperiodic function #Saddle-node bifurcation #Stability (learning theory) #Statistical physics #Transcritical bifurcation #math.DS #msc:34C15 #msc:34C55 #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1606.07307
published in arXiv (Cornell University) (Cornell University) · 13 pages, 13 figures
openalex publication_date 2016/06/23 · arxiv created 2016/09/19 · arxiv updated 2016/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and periodic bifurcations). For the first time, bifurcation diagrams are plotted using a feedback mechanism. It is shown that the stability curves and bifurcation diagrams must be dealt with simultaneously in order to fully understand the dynamics of the systems involved. Synaptic weights, biases and gradients of transfer functions are varied and the system is shown to be history dependent. The work can be applied to artificial neural networks and developing brains and gives a very important generalization of previous work in this field.