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Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model. (English) Zbl 1017.92041
Summary: Hopf bifurcation is demonstrated in an interacting one-predator-two-prey model with harvesting of the predator at a constant rate. Here the harvest rate is used as a control parameter. It is found that periodic solutions arise from stable stationary states when the harvest rate exceeds a certain limit. The stability of these periodic solutions is investigated with the variation of this control parameter. The approach is analytic in nature and the normal form analysis of the model is performed.

MSC:
92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
93C95 Application models in control theory
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[1] Azar, C.; Holmberg, J.; Lindgren, K., Stability analysis of harvesting in a predator-prey model, J. theoret. biol., 174, 13-19, (1995)
[2] Parrish, J.D.; Saila, S.B., Interspecific competition, predation and species diversity, J. theoret. biol., 27, 207-220, (1970)
[3] Takeuchi, Y.; Adachi, N., Existence and bifurcation of stable equilibrium in two-prey, one-predator communities, Bull. math. biol., 45, 877-900, (1983) · Zbl 0524.92025
[4] Fujii, K., Complexity – stability relationship of two-prey – one-predator species system model: local and global stability, J. theoret. biol., 69, 613-623, (1977)
[5] Hassard, B.D.; Kazarinoff, N.D.; Wan, Y.-H., Theory and applications of Hopf bifurcation, (1981), Cambridge University Press Cambridge · Zbl 0474.34002
[6] Wiggins, S., Introduction to applied nonlinear dynamical systems and chaos, (1990), Springer New York · Zbl 0701.58001
[7] Rosenzweig, M.L., Science, 177, 904, (1972)
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