Analysis of the power law logistic population model with slowly varying coefficients |
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Authors: | JJ Shepherd A Stacey T Grozdanovski |
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Institution: | 1. School of Mathematical and Geospatial Sciences, RMIT University, , Melbourne, 3001 Australia;2. School of life & Physical Sciences, RMIT University, , Melbourne, 3001 Australia |
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Abstract: | We apply a multiscale method to construct general analytic approximations for the solution of a power law logistic model, where the model parameters vary slowly in time. Such approximations are a useful alternative to numerical solutions and are applicable to a range of parameter values. We consider two situations—positive growth rates, when the population tends to a slowly varying limiting state; and negative growth rates, where the population tends to zero in infinite time. The behavior of the population when a transition between these situations occurs is also considered. These approximations are shown to give excellent agreement with the numerical solutions of test cases. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | logistic multiscaling population |
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