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In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem ($u_{1}\equiv0 $) has a unique positive solution $\left( \overline{u_{2}},\overline{u_{3}} \right).$ By using the birth rate of the prey $r_{1}$ as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set $\left( r_{1},\left( 0,\overline{ u_{2}},\overline{u_{3}}\right) \right) $ is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.
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참고문헌 (27)
참고문헌 신청
Herbert Amann / 1976 / Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces / SIAM Review 18(4):620~709
J. Blat / 1984 / Bifurcation of steady-state solutions in predator-prey and competition systems / Proceedings of the Royal Society of Edinburgh: Section A Mathematics 97:21~34
J. Blat / 1986 / Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations / SIAM Journal on Mathematical Analysis 17(6):1339~1353
Chuang-Hsiung Chiu / 1998 / Extinction of top-predator in a three-level food-chain model / Journal of Mathematical Biology 37(4):372~380
E. Conway / 1982 / Stability and bifurcation of steady-state solutions for predator-prey equations / Advances in Applied Mathematics 3(3):288~334
J. Blat / 1984 / Bifurcation of steady-state solutions in predator-prey and competition systems / Proceedings of the Royal Society of Edinburgh: Section A Mathematics 97:21~34
J. Blat / 1986 / Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations / SIAM Journal on Mathematical Analysis 17(6):1339~1353
Chuang-Hsiung Chiu / 1998 / Extinction of top-predator in a three-level food-chain model / Journal of Mathematical Biology 37(4):372~380
E. Conway / 1982 / Stability and bifurcation of steady-state solutions for predator-prey equations / Advances in Applied Mathematics 3(3):288~334
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