Abstract
This paper deals with the single neuron model involving delay-dependent parameters proposed by Xu et al. [Phys. Lett. A, 354, 126-136, 2006]. The dynamics of this model are still largely undetermined, and in this paper, we perform some bifurcation analysis to the model. Unlike the article [Phys. Lett. A, 354, 126-136, 2006], where the delay is used as the bifurcation parameter, here we will use range parameter as bifurcation parameter. Based on the linear stability approach and bifurcation theory, sufficient conditions for the bifurcated periodic solution are derived, and critical values of Hopf bifurcation are assessed. The amplitude of oscillations always increases as the range parameter increases; the robustness of period against change in the range parameter occurs.
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Xiao, M., Cao, J. (2010). Range Parameter Induced Bifurcation in a Single Neuron Model with Delay-Dependent Parameters. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_2
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DOI: https://doi.org/10.1007/978-3-642-13278-0_2
Publisher Name: Springer, Berlin, Heidelberg
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