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Bifurcation Analysis of Time-Delayed Jerk Model | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 مهر 1404 اصل مقاله (7.97 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66505.3108 | ||
| نویسندگان | ||
| Elahe Rafiean Borujeni1؛ Javad Alidousti* 1؛ Khayyam Salehi2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran. | ||
| 2Department of Computer Science, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran. | ||
| چکیده | ||
| This paper presents a comprehensive investigation into the dynamic behavior of a time- delayed jerk model. The study introduces an innovative approach to delayed feedback control, thoroughly examining the effects of delay on the system’s dynamics. The findings reveal that the presence of delay can lead to the emergence of previously unrecognized dynamic phenomena, such as Hopf, Bautin, and double-Hopf bifurcations. By employ- ing the normal form method, the coefficients for the normal forms of each bifurcation are determined, highlighting that the inclusion of delay significantly increases the sys- tem’s complexity. Numerical simulations are conducted to validate the effectiveness of the proposed delayed feedback control system, demonstrating its high accuracy in managing complex and nonlinear dynamics. This study offers an in-depth analysis of the system’s dynamic behavior while considering two distinct parameters, including co-dimension 1, co-dimension 2 analyses, and the basin of attraction. Poincaré sections and Lyapunov ex- ponents serve as essential tools for exploring the system’s dynamic behavior. The findings of this research can assist designers and engineers in effectively addressing delay effects in the design of mechanical and electrical systems, thereby enhancing the performance of dynamic systems. | ||
| کلیدواژه‌ها | ||
| Bifurcation؛ Double-Hopf؛ Bautin؛ Delay؛ Lyapunov exponent | ||
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