Open AccessBogdanov–Takens bifurcation in a neutral BAM neural networks model with delays
Author(s) -
Wang Runxia,
Liu Haihong,
Feng Fei,
Yan Fang
Publication year - 2017
Publication title -
iet systems biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.367
H-Index - 50
eISSN - 1751-8857
pISSN - 1751-8849
DOI - 10.1049/iet-syb.2017.0018
Subject(s) - homoclinic orbit , homoclinic bifurcation , bogdanov–takens bifurcation , mathematics , bifurcation , biological applications of bifurcation theory , saddle node bifurcation , bifurcation diagram , center manifold , singularity , heteroclinic bifurcation , fixed point , mathematical analysis , hopf bifurcation , physics , nonlinear system , quantum mechanics
In this study, the authors first discuss the existence of Bogdanov–Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second‐order and the third‐order normal forms of the Bogdanov–Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non‐trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non‐trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov–Takens bifurcation critical point.