Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects |
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Authors: | Seshadev Padhi PDN Srinivasu G Kiran Kumar |
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Institution: | 1. Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, India;2. Department of Mathematics, Andhra University, Visakhapatnam, India |
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Abstract: | In this article the minimum number of positive periodic solutions admitted by a non-autonomous scalar differential equation is estimated. This result is employed to find the minimum number of positive periodic solutions admitted by a model representing dynamics of a renewable resource that is subjected to Allee effects in a seasonally varying environment. The Allee effect refers to a decrease in population growth rate at low population densities. Leggett–Williams multiple fixed point theorem is used to establish the existence of positive periodic solutions. |
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