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Zamani Bahabadi, Alireza, Salehi Yekta, Masoumeh, Sadeghi Bajestani, Ghasem. (1405). Nonlinear Control of Hopf Bifurcation Type in the Rulkov Map Model: Analytical and Numerical Study. پژوهشنامه مدیریت اجرایی, (), -. doi: 10.22080/cjms.2026.31672.1845
Alireza Zamani Bahabadi; Masoumeh Salehi Yekta; Ghasem Sadeghi Bajestani. "Nonlinear Control of Hopf Bifurcation Type in the Rulkov Map Model: Analytical and Numerical Study". پژوهشنامه مدیریت اجرایی, , , 1405, -. doi: 10.22080/cjms.2026.31672.1845
Zamani Bahabadi, Alireza, Salehi Yekta, Masoumeh, Sadeghi Bajestani, Ghasem. (1405). 'Nonlinear Control of Hopf Bifurcation Type in the Rulkov Map Model: Analytical and Numerical Study', پژوهشنامه مدیریت اجرایی, (), pp. -. doi: 10.22080/cjms.2026.31672.1845
Zamani Bahabadi, Alireza, Salehi Yekta, Masoumeh, Sadeghi Bajestani, Ghasem. Nonlinear Control of Hopf Bifurcation Type in the Rulkov Map Model: Analytical and Numerical Study. پژوهشنامه مدیریت اجرایی, 1405; (): -. doi: 10.22080/cjms.2026.31672.1845

Nonlinear Control of Hopf Bifurcation Type in the Rulkov Map Model: Analytical and Numerical Study

Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 آبان 1405
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.31672.1845
نویسندگان
Alireza Zamani Bahabadi* 1؛ Masoumeh Salehi Yekta2؛ Ghasem Sadeghi Bajestani3
1Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
2Department of Mathematics, Ferdowsi University of Mashhad, Iran
3Department of Medical Engineering, Imam Reza International University, Mashhad, Iran
تاریخ دریافت: 14 اردیبهشت 1405،  تاریخ بازنگری: 01 تیر 1405،  تاریخ پذیرش: 15 شهریور 1405 
چکیده
Changing the bifurcation type is an important approach for controlling the qualitative behavior of nonlinear dynamical systems. In this paper, a nonlinear washout filter controller is proposed to modify the type of Hopf bifurcation in the Rulkov map model. By introducing the controller, the original system is transformed into a three-dimensional discrete-time dynamical system. The center manifold theory and normal form theory are employed to derive the reduced dynamics near the bifurcation point and to analytically determine the influence of the control gain on the Hopf bifurcation characteristics. The analytical results show that the proposed controller modifies the first Lyapunov coefficient and can change the Hopf bifurcation from subcritical to supercritical through an appropriate selection of the control parameter.
Consequently, the stability properties of the invariant Hopf circle are altered, leading to the suppression of undesirable oscillatory behavior. Numerical simulations, including phase spaces and time-series responses, confirm the theoretical predictions and demonstrate excellent agreement with the analytical results. The results demonstrate that the proposed
control method is effective for regulating bifurcation behavior and stabilizing the dynamics of the Rulkov neuron model. This approach may provide useful insights into the suppression of abnormal oscillations in discrete-time neuronal systems.
کلیدواژه‌ها
Rulkov map model؛ Discrete-time system؛ Washout filter؛ Control of Hopf bifurcation؛ Normal form
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