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Javidmanesh, Elham, Zamani Bahahbadi, Alireza. (1401). Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons. فیزیولوژی و بیوتکنولوژی آبزیان, 11(1), 19-34. doi: 10.22124/jmm.2022.22299.1972
Elham Javidmanesh; Alireza Zamani Bahahbadi. "Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons". فیزیولوژی و بیوتکنولوژی آبزیان, 11, 1, 1401, 19-34. doi: 10.22124/jmm.2022.22299.1972
Javidmanesh, Elham, Zamani Bahahbadi, Alireza. (1401). 'Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons', فیزیولوژی و بیوتکنولوژی آبزیان, 11(1), pp. 19-34. doi: 10.22124/jmm.2022.22299.1972
Javidmanesh, Elham, Zamani Bahahbadi, Alireza. Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 11(1): 19-34. doi: 10.22124/jmm.2022.22299.1972

Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons

Journal of Mathematical Modeling
دوره 11، شماره 1، خرداد 2023، صفحه 19-34    اصل مقاله (316.76 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2022.22299.1972
نویسندگان
Elham Javidmanesh1؛ Alireza Zamani Bahahbadi* 2
1Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده
In this paper, a general class of fractional-order complex-valued bidirectional associative memory neural network with time delay is considered. This neural network model contains an arbitrary number of neurons, i.e. one neuron in the X-layer and other neurons in the Y-layer. Hopf bifurcation analysis of this system will be discussed. Here, the number of neurons, i.e., $n$ can be chosen arbitrarily. We study Hopf bifurcation by taking the time delay as the bifurcation parameter. The critical value of the time delay for the occurrence of Hopf bifurcation is determined. Moreover, we find two kinds of appropriate Lyapunov functions that under some sufficient conditions, global stability of the system is obtained. Finally, numerical examples are also presented.
کلیدواژه‌ها
neural network؛ fractional ordinary differential equations؛ Hopf bifurcation؛ time delay؛ Lyapunov function
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تعداد مشاهده مقاله: 218
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