Figure 1. The graphs of the function u(t) and the function v(t) for the model (1) with α = 2, β = 1, γ = −0:5, and u(0) = 3, v(0) = 1
Figure 2. The phase plane behavior of (u(t); v(t)) for the model (1) with α = 2, β = 1, γ = −0:5, and u(0) = 3, v(0) = 1
Figure 3. The graphs of the function u(t) and the function v(t) for the model (1) with α = 4, β = 1, γ = −0:5, and u(0) = 3, v(0) = 1
Figure 4. The phase plane behavior of (u(t); v(t)) for the model (1) with α = 4, β = 1, γ = −0:5, and u(0) = 3, v(0) = 1
참고문헌
- M.E. Gilpin: Do hares eat lynx?. American Naturalist. 107 (1973), 727-730. https://doi.org/10.1086/282870
- C. Holling: The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Entomol. 91 (1959), 293-320. https://doi.org/10.4039/Ent91293-5
- C. Holling: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 45 (1965), 3-60.
- C. Jost, G. Devulder, J.A. Vucetich, R. Peterson & R. Arditi: The wolves of Isle Royale display scale-invariant satiation and density dependent predation on moose. J. Anim. Ecol. 74 (2005), no. 5, 809-816. https://doi.org/10.1111/j.1365-2656.2005.00977.x
- A.J. Lotka: Contribution to the Theory of Periodic Reaction. J. Phys. Chem. 14 (1910), no. 3, 271-274.
- A.J. Lotka: Analytical Note on Certain Rhythmic Relations in Organic Systems. Proc. Natl. Acad. Sci. U.S.A. 6 (1920), 410-415. https://doi.org/10.1073/pnas.6.7.410
- M.L. Rosenzweig & R.H. MacArthur: Graphical representation and stability conditions of predator-prey interactions. American Naturalist. 97 (1963), 209-223. https://doi.org/10.1086/282272
- S. Shim: Hopf Bifurcation Properties og Holling Type Predator-Prey System. J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 15 (2008), no. 3, 329-342.