Hybrid control on bifurcation for a delayed fractional gene regulatory network |
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| Institution: | 1. Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing 210096, China;2. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;1. School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang 441053, China;2. Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing 210096, China;3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;2. College of Mathematic Science, Liaocheng University, Liaocheng 252000, China;1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;2. School of Computing, Engineering and Mathematics, Western Sydney University, Penrith NSW 2751, Australia;3. School of Economics & Management, Southeast University, Nanjing 210096, China;4. School of Mathematics, Southeast University, Nanjing 210096, China |
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| Abstract: | A novel delayed fractional-order gene regulatory network model is proposed in this paper. Firstly, the sum of delays is chosen as the bifurcation parameter, the conditions of the existence for the Hopf bifurcation are obtained by analyzing the associated characteristic equation. Then, it is the first time that a hybrid controller is designed to control the Hopf bifurcation for the proposed network. It is demonstrated that both fractional order and feedback gain can effectively control the dynamics of such network, the stability domain can be extended under the small fractional order or feedback gain. The controller is enough to delay the onset of the Hopf bifurcation and achieve some desirable dynamical behaviors by changing the appropriate order or feedback gain. Finally, numerical simulations are employed to justify the validity of our theoretical analysis. |
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