Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay |
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| Authors: | Abdulaziz Alofi Fengli Ren Abdullah Al-Mazrooei Ahmed Elaiw Jinde Cao |
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| Institution: | Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia ;Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 China ;Department of Mathematics, Southeast University, Nanjing, 210096 China ;Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah, 21589 Saudi Arabia |
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| Abstract: | In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results. |
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| Keywords: | Power-rate synchronization Genetic oscillators Unbounded time-varying delay Matrix inequality |
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