Asymptotic solution of wave front of the telegraph model of dispersive variability |
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| Institution: | 1. Materials Genome Institute, Shanghai University, Shanghai 200444, China;2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, China;3. Department of Mathematics, Shanghai University, Shanghai 200444, China;1. School of Mathematics and Physics, University of Science and Technology Beijing, China;2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | A number of nonlinear phenomena in physical, chemical, economical and biological processes are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper we use the technique of asymptotic solution to find travelling wave solution for the telegraph model of dispersive variability which is a generalization of the Julian Cook model. Our model tackled special values of the time delay and the probability that an individual is disperser in a population of dispersers and nondispersers. The solution of our model is reduced to telegraph Fisher–Kolmogoroff invasion and Julian Cook models. Also, the effect of the time delay on the propagation speed is presented. |
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