Coupled logistic carrying capacity model

Mohd Safuan, Hamiza ; Towers, Isaac ; Jovanoski, Zlatko ; Sidhu, Harvinder

ANZIAM Journal, Tome 52 (2012), / Harvested from Australian Mathematical Society

Résumé

This study proposes a coupled nonlinear system based on the logistic equation that models the interaction of a population with its time varying environment. The model eliminates the need for a priori knowledge of the environmental carrying capacity or constraints to be placed upon the initial conditions. Analysis and computer simulations are presented to illustrate the system's dynamical behaviour. References R. B. Banks. Some Basic Frameworks. In F. John, J. E. Marsden, L. Sirovich, M. Golubitsky and W. Jager (Eds.). Growth and Diffusion Phenomena:Mathematical Frameworks and Applications, {5--6, Springer-Verlag, Berlin, Germany, 1994.} S. Ikeda and T. Yokoi. {Fish population dynamics under nutrient enrichment---A case of the {E}ast {S}eto Inland Sea.} Ecological Modelling, 10, 141--165, 1980. doi:10.1016/0304-3800(80)90057-5 C. V. Trappey and H. Y. Wu. {An evaluation of the time--varying extended logistic, simple logistic, and Gompertz models for forecasting short product lifecycles.} Advanced Engineering Informatics, 22, 421--430, 2008. doi:10.1016/j.aei.2008.05.007 S. P. Rogovchenko and Y. V. Rogovchenko. {Effect of periodic environmental fluctuations on the {P}earl-{V}erhulst model.} Chaos, Solitons and Fractals, 39, 1169--1181, 2009. doi:10.1016/j.chaos.2007.11.002 H. Safuan, I. N. Towers, Z. Jovanoski and H. S. Sidhu. {A simple model for the total microbial biomass under occlusion of healthy human skin.} {In Chan, F., Marinova, D. and Anderssen, R.S. (eds) MODSIM2011, 19th International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand., 733--739, 2011.} P. Meyer. {Bi-logistic Growth.} Technological Forecasting and Social Change, 47, 89--102, 1994. doi:10.1016/0040-1625(94)90042-6 P. Meyer and J. H. Ausubel. {Carrying Capacity: {A} Model with Logistically Varying Limits.} Technological Forecasting and Social Change, 61, 209--214, 1999. doi:10.1016/S0040-1625(99)00022-0 R. Huzimura and T. Matsuyama. {A mathematical model with a modified logistic approach for singly peaked population processes.} Theoretical Population Biology, 56, 301--306, 1999. doi:10.1006/tpbi.1999.1426 J. H. M. Thornley and J. France. {An open-ended logistic-based growth function.} Ecological Modelling, 184, 257--261, 2005. doi:10.1016/j.ecolmodel.2004.10.007 J. H. M. Thornley, J. J. Shepherd and J. France. {An open-ended logistic-based growth function: Analytical solutions and the power-law logistic model.} Ecological Modelling, 204, 531--534, 2007. doi:10.1016/j.ecolmodel.2006.12.026

Détail

Publié le : 2012-01-01
DOI : https://doi.org/10.21914/anziamj.v53i0.4972