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Stability and Hopf bifurcation in leech heart interneuron model | ||
Iranian Journal of Numerical Analysis and Optimization | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 29 تیر 1401 اصل مقاله (3.83 M) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.22067/ijnao.2022.75087.1101 | ||
نویسندگان | ||
Fatemeh Parvizi* 1؛ Mohammad Reza Razvan2؛ Yousef Alipour Fakhri1 | ||
1Department of Mathematics, Payame Noor University(PNU), P. O. Box 19395-4697, Tehran, Iran | ||
2Department of Mathematics, Faculty of Mathematical Sciences, University of Sharif, Tehran, Iran. | ||
چکیده | ||
This article investigates the activity regimes of a realistic neuron model (as a slow-fast system). The authors study this model using the dynamical systems theory e.g., qualitative theory methods of slow-fast systems. The authors obtain the stability conditions of equilibria in leech heart interneurons under defined pharmacological conditions and following Hodgkin-Huxley formalism. Although in neuronal models, the membrane is usually considered capacitance as a fixed parameter, the membrane capacitance parameter is assumed as a control parameter to guarantee the existence of Hopf bifurcation using the Routh-Hurwitz criteria. The authors investigate transition mechanism between the silent phase and tonic spiking mode. Furthermore, some simulations are provided using XPPAUT software for analytical results. | ||
کلیدواژهها | ||
Stability؛ Hopf bifurcation؛ Routh-Hurwitz criteria | ||
آمار تعداد مشاهده مقاله: 144 تعداد دریافت فایل اصل مقاله: 35 |