Hopf Bifurcation of a Type of Neuron Model with Multiple Time Delays
2019 ◽
Vol 29
(12)
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pp. 1950163
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Keyword(s):
By applying a geometrical scheme developed to tackle the eigenvalue problem of delay differential equations with multiple time delays, Hopf bifurcation of Hopfield neuron model is analyzed in two-parameter space. By the introduction of two new angles, the calculation of imaginary roots is carried out analytically and effectively. By increasing the parameter to cross over the Hopf bifurcation lines, the stability switching direction is confirmed. The method is a useful tool to show the partition of stable and unstable regions in two-parameter space and detect double Hopf bifurcation further. The typified dynamical behaviors based on nearby double Hopf points are analyzed by applying the normal form technique and center manifold method.
2016 ◽
Vol 26
(11)
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pp. 1650187
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2012 ◽
Vol 45
(11)
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pp. 1387-1396
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2003 ◽
Vol 2003
(4)
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pp. 137-152
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2020 ◽
Vol 131
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pp. 109483
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Keyword(s):
2001 ◽
Vol 32
(4)
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pp. 409-412
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Keyword(s):
2021 ◽
Vol 15
◽
pp. 121-127
Keyword(s):
Keyword(s):
2020 ◽
Vol 30
(05)
◽
pp. 2050069