Codimension two bifurcation in a simple delayed neuron model

Codimension two bifurcation in a simple delayed neuron model

This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model c...

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Veröffentlicht in:Neural computing & applications 2013-12, Vol.23 (7-8), p.2295-2300
Hauptverfasser: He, Xing, Li, Chuandong, Huang, Tingwen, Peng, Mei
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Artificial Intelligence
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Computer science
control theory
systems
Connectionism. Neural networks
Data Mining and Knowledge Discovery
Differential geometry
Exact sciences and technology
Geometry
Global analysis, analysis on manifolds
Image Processing and Computer Vision
Mathematics
Original Article
Probability and Statistics in Computer Science
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung:This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model can exhibit pitchfork, Hopf, homoclinic bifurcation and saddle node bifurcation of periodic orbits. Some numerical simulations are given to support the analytic results.
ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-012-1181-1