DIFFUSION INDUCED SHIFT OF BIFURCATION POINT IN A MANGROVE ECOSYSTEM FOOD‐CHAIN MODEL WITH HARVESTING |
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Authors: | B MUKHOPADHYAY R BHATTACHARYYA |
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Institution: | 1. Department of Science, Central Calcutta Polytechnic, 21, Convent Road, Calcutta 700014, India E‐mail: banibrat001@yahoo.co.in;2. Department of Science, The Calcutta Technical School, 110, S.N. Banerjee Road, Calcutta 700013, India E‐mail: rakhi_bhattach@yahoo.co.in |
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Abstract: | Abstract The present paper deals with a detritus‐based food‐chain model within a mangrove ecosystem. The top predator (mainly fish) is assumed to have a commercial value and undergoes harvesting. Stability and bifurcation behavior of the model is studied and a threshold harvest rate is obtained. Next we introduce environmental nonhomogenity into the model equation. The resulting reaction diffusion system is investigated, and the criteria for supercritical Hopf bifurcation is obtained using the method of Lyapunov first coefficient. A comparison of the critical harvest rates under the homogeneous and the nonhomogeneous context is performed both analytically and numerically. |
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Keywords: | Detritus detritivore harvesting diffusion Hopf bifurcation standing waves |
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