title: Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay.
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.
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
authors.forename: Abdulaziz
authors.initials: A
authors.lastname: Alofi
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 China.
authors.forename: Fengli
authors.initials: F
authors.lastname: Ren
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia ; Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah, 21589 Saudi Arabia.
authors.forename: Abdullah
authors.initials: A
authors.lastname: Al-Mazrooei
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
authors.forename: Ahmed
authors.initials: A
authors.lastname: Elaiw
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia ; Department of Mathematics, Southeast University, Nanjing, 210096 China.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
keywords: Genetic oscillators; Matrix inequality; Power-rate synchronization; Unbounded time-varying delay