Coupled logistic carrying capacity model

Abstract

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