We consider the existence of multiple positive solutions to the steady state reaction diffusion equation with Dirichlet boundary conditions of the form: {-u″=λ[u-u2/K-cu2/1+ u2-∈], x ∈ (0,1) u(0)=0=u(1). Here 1/λ is the diffusion coefficient and K, c and are positive constants. This model describes the steady states of a logistic growth model with grazing and constant yield harvesting in a spatially homogeneous ecosystem. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. In this paper, we discuss the occurrence of a Σ-shaped bifurcation diagram for positive solutions. In particular, for certain parameter values of c,K, ∈ and the diffusion coefficient, we prove the existence of at least four positive solutions. We prove our results by the quadrature method. © 2011 Elsevier Ltd. All rights reserved.}, author_keywords={Σ-shaped bifurcation curves; Ecological systems; Grazing and constant yield harvesting}, keywords={Bifurcation curves; Bifurcation diagram; Dirichlet boundary condition; Ecological models; Ecological systems; Fish populations; Grazing and constant yield harvesting; Logistic growth model; Multiple positive solutions; Parameter values; Positive constant; Positive solution; Quadrature methods; Steady state; Steady state reactions, Boundary conditions; Diffusion; Ecology; Equations of state; Fisheries; Harvesting; Partial differential equations; Potassium, Bifurcation (mathematics)}, references={Causey, R., Sasi, S., Shivaji, R., An ecological model with grazing and constant yield harvesting (2010) Bull. Belg. Math. Soc., 17 (5), pp. 833-839; Lee, E., Sasi, S., Shivaji, R., S-shaped bifurcation curves in ecosystems (2011) J. Math. Anal. Appl., , 10.1016/j.jmaa.2011.03.048; May, R.M., Thresholds and breakpoints in ecosystems with a multiplicity of stable states (1977) Nature, 269, pp. 471-477; Noy-Meir, I., Stability of grazing systems an application of predatorprey graphs (1975) J. Ecol., 63, pp. 459-482; Oruganti, S., Shi, J., Shivaji, R., Diffusive equations with constant yield harvesting, I: Steady states (2002) Trans. Amer. Math. Soc., 354, pp. 3601-3619; Steele, J.H., Henderson, E.W., Modeling long-term fluctuations in fish stocks (1984) Science, 224 (4652), pp. 985-987; Brauer, F., Castillo-Chavez, C., (2001) Mathematical Models in Population Biology and Epidemiology, 40. , Texts in Applied Mathematics Springer-Verlag New York; Clark, C.W., (1990) Mathematical Bioeconomics, the Optimal Management of Renewable Resources, , John Wiley & Sons, Inc. New York; Brown, K.J., Ibrahim, M.M.A., Shivaji, R., S-shaped bifurcation curves (1981) Nonlinear Anal. TMA, 5 (5), pp. 475-486; Laetsch, T., The number of solutions of a nonlinear two point boundary value problem (1970) Indiana Univ. Math. J., 20 (1), pp. 1-13; Jiang, J., Shi, J., Bistability dynamics in some structured ecological models (2009) Spatial Ecology, pp. 33-62. , R.S. Cantrell, C. Cosner, S. Ruan, Chapman & Hall, CRC Mathematical and Computational Biology}, correspondence_address1={Shivaji, R.; Department of Mathematics and Statistics, , Greensboro, NC 27412, United States; email: shivaji@uncg.edu}, issn={14681218}, language={English}, abbrev_source_title={Nonlinear Anal. Real World Appl.}, document_type={Article}, source={Scopus},