An analytical solution for a nonlinear time-delay model in biology |
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| Authors: | Hina Khan Shi-Jun Liao RN Mohapatra K Vajravelu |
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| Institution: | 1. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;2. Dept. of Mathematics, University of Central Florida, Orlando, FL 32816, USA;1. College of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, P.R. China;2. School of Automation, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, P.R. China;1. Sino-French Int. Joint Lab. of Automation and Signals (LaFCAS), Automation School, Nanjing University of Science and Technology, Nanjing 210094, China;2. Laboratories of LaFCAS and LAGIS, Lille University of Science and Technology, France;1. Department of Mathematics, Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, Jeddah, Saudi Arabia;2. Department of Mathematics, Faculty of Science—Blqarn Campus, Bisha University, Saudi Arabia;3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, PR China;4. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa;5. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah-21589, Saudi Arabia;1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China |
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| Abstract: | In this paper, the homotopy analysis method is applied to develop a analytic approach for nonlinear differential equations with time-delay. A nonlinear model in biology is used as an example to show the basic ideas of this analytic approach. Different from other analytic techniques, the homotopy analysis method provides a simple way to ensure the convergence of the solution series, so that one can always get accurate approximations. A new discontinuous function is defined so as to express the piecewise continuous solutions of time-delay differential equations in a way convenient for symbolic computations. It is found that the time-delay has a great influence on the solution of the time-delay nonlinear differential equation. This approach has general meanings and can be applied to solve other nonlinear problems with time-delay. |
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