Dynamical Analysis of a Tri‐Neuron Fractional Network |
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| Authors: | Cheng‐dai Huang Jin‐de Cao Min Xiao Ahmed Alsaedi Fuad E. Alsaadi Tasawar Hayat |
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| Affiliation: | 1. Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing, China;2. School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang, China;3. School of Mathematics and Statistics, Shandong Normal University, Ji'nan, China;4. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China;5. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;6. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;7. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;8. Department of Mathematics, Quaid‐I‐Azam University, Islamabad, Pakistan |
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| Abstract: | The present paper concerns with the dynamics of a fractional neural network involving three neurons. Firstly, the bifurcation point is identified for which Hopf bifurcations may occur by taking the system parameter as a bifurcation parameter via the stability analysis of fractional systems. It is indicated that the system parameter can significantly affect the dynamical properties of such network. Secondly, the impact of the order on the bifurcation point is carefully examined. It is found that the occurrence of bifurcation is delayed as the order increases as long as the other system parameters are established. Finally, a numerical example is exploited to verify the efficiency of theoretical results. |
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| Keywords: | Fractional order stability Hopf bifurcation system parameter neural networks |
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