Open AccessDYNAMICS OF A SINGLE MODEL NEURON
Author(s) -
Frank Pasemann
Publication year - 1993
Publication title -
international journal of bifurcation and chaos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.761
H-Index - 103
eISSN - 1793-6551
pISSN - 0218-1274
DOI - 10.1142/s0218127493000210
Subject(s) - dynamics (music) , biological neuron model , nonlinear system , mathematics , connection (principal bundle) , period doubling bifurcation , bifurcation , cusp (singularity) , statistical physics , control theory (sociology) , physics , computer science , geometry , artificial neural network , control (management) , quantum mechanics , artificial intelligence , acoustics , machine learning
The parametrized dynamics of a standard nonlinear model neuron with self-interaction is discussed. For units with a self-excitatory connection a hysteresis effect is observed, and the underlying mechanism is identified as that of a cusp catastrophe. This is true for discrete as well as for continuous dynamics. For the discrete dynamics of self-inhibiting units there appear period-doubling bifurcations from stationary states to stable period-2 orbits.
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