Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
hidden prey; explicit prey; bifurcation; predator-prey model
Summary:
The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.
References:
[1] Chakraborty, K., Das, S. S.: Biological conservation of a prey-predator system incorporating constant prey refuge through provision of alternative food to predators: A theoretical study. Acta Biotheoretica 62 (2014), 183-205. DOI 10.1007/s10441-014-9217-9
[2] Clark, C. W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley-Interscience Publication, John Wiley & Sons, New York (1990). MR 1044994 | Zbl 0712.90018
[3] Assis, L. M. E. de, Banerjee, M., Venturino, E.: Comparing predator-prey models with hidden and explicit resources. Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 64 (2018), 259-283. DOI 10.1007/s11565-018-0298-2 | MR 3857003
[4] Assis, L. M. E. de, Banerjee, M., Venturino, E.: Comparison of hidden and explicit resources in ecoepidemic models of predator-prey type. (to appear) in Comput. Appl. Math.
[5] Freedman, H. I.: Deterministic Mathematical Models in Population Ecology. Monographs and Textbooks in Pure and Applied Mathematics 57, Marcel Dekker, New York (1980). DOI 10.2307/3556198 | MR 0586941 | Zbl 0448.92023
[6] Goel, N. S., Maitra, S. C., Montroll, E. W.: On the Volterra and other nonlinear models of interacting populations. Rev. Mod. Phys. 43 (1971), 231-276. DOI 10.1103/RevModPhys.43.231 | MR 0484546
[7] Haque, M., Li, B. L., Rahman, M. S., Venturino, E.: Effect of a functional response-dependent prey refuge in a predator-prey model. Ecological Complexity 20 (2014), 248-256. DOI 10.1016/j.ecocom.2014.04.001
[8] Haque, M., Rahman, M. S., Venturino, E.: Comparing functional responses in predator-infected eco-epidemics models. BioSystems 114 (2013), 98-117. DOI 10.1016/j.biosystems.2013.06.002
[9] Hixon, M. A.: Species diversity: Prey refuges modify the interactive effects of predation and competition. Theor. Popul. Biol. 39 (1991), 178-200. DOI 10.1016/0040-5809(91)90035-E
[10] Lotka, A. J.: Contribution to the theory of periodic reactions. J. Phys. Chem. 14 (1910), 271-274. DOI 10.1021/j150111a004
[11] Lotka, A. J.: Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. USA 6 (1920), 410-415. DOI 10.1073/pnas.6.7.410
[12] Murray, J. D.: Mathematical Biology. Biomathematics 19, Springer, Berlin (1989). DOI 10.1007/978-3-662-08539-4 | MR 1007836 | Zbl 0682.92001
[13] Perko, L.: Differential Equations and Dynamical Systems. Texts in Applied Mathematics 7, Springer, New York (2001). DOI 10.1007/978-1-4613-0003-8 | MR 1801796 | Zbl 0973.34001
[14] Venturino, E.: The influence of diseases on Lotka-Volterra systems. Rocky Mt. J. Math. 24 (1994), 381-402. DOI 10.1216/rmjm/1181072471 | MR 1270046 | Zbl 0799.92017
[15] Venturino, E.: Ecoepidemiology: a more comprehensive view of population interactions. Math. Model. Nat. Phenom. 11 (2016), 49-90. DOI 10.1051/mmnp/201611104 | MR 3452635 | Zbl 1384.92060
[16] Volterra, V.: Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Memorie Acdad. d. L. Roma 2 (1927), 31-113 Italian \99999JFM99999 52.0450.06.
[17] Volterra, V.: Variations and fluctuations of the number of individuals in animal species living together. ICES Journal of Marine Science 3 (1928), 3-5. DOI 10.1093/icesjms/3.1.3
Partner of
EuDML logo