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Stability and Hopf bifurcation analysis of a chaotic system using time-delayed feedback control method | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 1 - شماره پیاپی 24، فروردین 2023، صفحه 183-195 اصل مقاله (988.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19174.1219 | ||
| نویسندگان | ||
| Abdul Hussain Surosh* 1، 2؛ Reza Khoshsiar2؛ Javad Alidousti2 | ||
| 1Department of Mathematics, Baghlan University, Pol-e-Khomri, Baghlan - Afghanistan | ||
| 2Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran | ||
| چکیده | ||
| In this paper, we study the effect of delayed feedback on the dynamics of a three-dimensional chaotic dynamical system and stabilize its chaotic behavior and control the respective unstable steady state. We derive an explicit formula in which a Hopf bifurcation occurs under some analytical conditions. Then the existence and stability of the Hopf bifurcation are analyzed by considering the time delay $ \tau $ as a bifurcation parameter. Furthermore, by numerical calculation and appropriate ascertaining of both the feedback strength $ K $ and time delay $ \tau $, we find certain threshold values of time delay at which an unstable equilibrium of the considered system is successfully controlled. Finally, we use numerical simulations to examine the derived analytical results and reveal more dynamical behaviors of the system. | ||
| کلیدواژهها | ||
| Chaotic system؛ Chaos control؛ Time-delayed feedback؛ Stability؛ Hopf bifurcation | ||
| مراجع | ||
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