• Journal for History of Mathematics
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• v.24 no.2
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• pp.47-59
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• 2011

Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

• Journal of Wetlands Research
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• v.19 no.4
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• pp.523-532
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• 2017

Environmental problems in urban spaces tend to result from excessive use of resources faster than the ecosystem can recover itself. In order to address this problem, city or municipal governments tend to devise plans and policies to lead development within their ecological carrying capacity. This study computes ecological capacity of Asan city, Province Chung Nam, South Korea through applying the concept of ecological footprint. This study finds ecological footprint and deficit of Asan city in 2015 were 5.12 and -4.99, respectively. From 2001 to 2015, Asan city experienced not only an 81% increase of ecological footprint, but also a 190% increase of ecological deficit. Such results suggest that Asan city has experienced a steady increase of resource consumption due to population increase and urban growth, indicating that loss of ecological spaces such as green space, farmland, wetland and so on restoring the ecosystem has been accelerated. Therefore, in order to promote sustainable development, Asan city should not only protect green space, farmland, wetland, and so on but also create urban growth plans and policies taking into account its environmental capacity of the city. This study provides suggestions for Asan city to lead urban growth within its environmental capacity by applying ecological deficit.