Study on Jilin province's population growth trend model.
According to Jilin Statistical Yearbook , the population of Jilin province has increased by 17.303 million during the 61 years since the founding of our country. Its variation tendency mainly showed that while the total population kept growing. the growth rate was on a decline. Despite this trend. the growth rate in every 6 years was relatively stable. Besides. the gender ratio is heading toward balance. Moreover. on the one hand. agricultural population of Jilin province maintained a rapid and sustainable growth between the year 1949 and 1974. rising from 8.282 million to 14.198 million. However. the agricultural population rose slowly from the year 1974 to 2010. with a population of 14.198 million and 14.817 million respectively. On the other hand. the nonagricultural population is in constant increase. from 1.803 million in 1949 to 12.421 million in 2010. As the population increases. the nonagricultural trend is gaining momentum and presents a trend of linear growth.
Malthusian Population Model
The population growth rate is a constant. which means that the population increases exponentially with time passing by. The growth model is y = [x.sub.0][(i + r).sup.k], in which [x.sub.0] stands for the initial population. r the growth rate. k the year range. and y represents the total population in the final year k . Considering the development tendency of Jilin province as well as its population goal. this paper suggests that. by the year 2010. Jilin's total population scale will development be y = [x.sub.0]x[(1+r).sup.k], r = 0.37%. k = 1.2, .... This model conforms to the dynamic trend of Jilin's future population development in a large extent. Therefore. it is able to predict the population of Jilin province between the year 2001 and 2020 and it is estimated that the total population of Jilin province will have reached 28.288 billion by the year 2020 (See Table 1).
Logistic Model assumes that the function r(x), r(x) = r - sx, s > 0 is the decreasing function of the function x(t), and the linear function of x. Here r is tantamount to the growth rate r(x) < r when x(t = 0), namely the inherent population growth rate when the population is free from the constraint of the environment and resources, which is apparently the actual growth rate. In order to clarify the physical significance of the parameter s, this paper introduces the concept of maximum population. When x = [x.sub.m], the growth rate becomes 0, namely 0 = r - [sx.sub.m], s = r/[x.sub.m] Under the linear hypothesis of the Logistic, there exist the following models: dx/dt = r [1 - x/[x.sub.m]]x, X(0)= [x.sub.0]. According to Logistic Model, as long as we estimate the parameters [x.sub.m], a and b, we then can determine the concrete form of the population model . By using this method, we draw the conclusion that a = 1.83 and b = -0.06.
COMPARISON AND ANALYSIS OF MODELS
It can be observed that there is only a comparatively small error between Malthusian Population Model's predicted outcome of population and the actual population. The minimum error is 0.1 ten thousand people (in 2007), the maximum of the relative error is 0.26% (in 2005), and most of the relative errors are lower than 0.5%; therefore the actual predicted outcome is good . During population's natural growth, the net relative growth rate is a constant and the Logistic Population Model was accordingly established: if at the time t the population is x(t) from t to (t + [DELTA]t), the population growth is: x(t + [DELTA]t) - x(t) = rx(t)[DELTA]t, if [x.sub.0] = x(0), [DELTA]t [right arrow] 0, the solution: X = k/1+(k/[x.sub.0]-1)[e.sup.n] is got by solving a system of equations.
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A population system is a non-linear. open system. with the characteristic of dissipation structure; therefore stability criteria can be used to judge the stability of a population system. According to the dissipation structure theory. the stability of a system in a non-equilibrium linear region can be judged by the generation principle of minimum entropy dp/dt [less than or equal to] 0.  Therefore. if the population stability range of Jilin province can be controlled within 33 million. the net population growth rate can be stable. tending to be a zero population growth rate.
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Observed from the separate trends and proportions of Jilin Province's agricultural and non-agricultural population. the trend of non-agriculturalization in Jilin province is enlarging. which means that the urbanization process in Jilin is speeding up. Until 2004, non-agricultural population growth trend had been almost the same with years before. Known from Jilin Province's gender ratio. male population and female population are balancing. both towards a proportion of 50%.
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As population growth and population prediction are influenced by multi-aspects. the real population growth process can never be embodied or predicted by a specific model. The model depends on the specific situation. Both Malthusian Population Model and Logistic Model can meet requirement of precision in predicting the population growth of Jilin province. Malthusian Population Model and Logistic Model are applied in this article to predict population growth of Jilin province. Therefore. the population stability range of Jilin province is within 33 million. After the year 1950. Jilin province witnesses a zero net population growth rate which is quite stable.
 Jilin Bureau of Statistics. Statistical Yearbook: 1949-2010. Changchun: Jilin Statistics Press.
 JIANG. Qiyuan et al. (2003). Mathematical Model (3rd ed., pp. i27-i38). Beijing: Higher Education Press.
 LIU. Weiguo (2005). MATLAB Program Design Course (pp. 107-113). China Water Power Press.
 WANG. Nengchao (2005). Computational Method Algorithm Design and MATLAB (pp. 78-83). Higher Education Press.
 XU. Liwei (2003). The Convergence of Period-doubling on Logistic Model. College Mathematics, 19(6),108-113.
JIN Yuzi [a], *
[a] Associate Professor, Department of Mathematics, Jilin Institute of Chemical Technology, China.
* Corresponding author.
Received 10 October 2012; accepted 18 December 2012
JIN Yuzi (2012). Study on Jilin Province's Population Growth Trend Model. Advances in Natural Science, 5(4), 52-54. Available from: http:// www.cscanada.net/index.php/ans/article/view/j.ans.1715787020120504. ZJ001 DOI: http://dx.doi.org/10.3968/j.ans.1715787020120504.ZJ001
Table 1 The Prediction of Jilin's Population Between the Year 2001 and 2020 (10 Thousand) Year Total population 2001 2637.1 2002 2646.9 2003 2656.7 2004 2666.5 2005 2676.3 2006 2686.2 2007 2696.2 2008 2706.2 2009 2716.2 2010 2726.2 2011 2736.3 2012 2746.4 2013 2756.6 2014 2766.8 2015 2777.0 2016 2787.3 2017 2797.6 2108 2808.0 2019 2818.4 2020 2828.8 Table 2 Comparison of All Models' Prediction outcomes Unit (Ten thousand) Malthusian model Year Actual population Predicted Relative error population 2001 2637.1 2637.1 0.00% 2002 26h9.4 2646.9 0.13% 2003 2658.6 2656.7 0.08% 2004 2661.9 2666.5 0.17% 2005 2669.4 2676.3 0.26% 2006 2679.5 2686.2 0.25% 2007 2696.1 2696.2 0.1% 2008 2710.5 2706.2 0.16% 2009 2719.5 2716.2 0.12% 2010 2723.8 2726.2 0.08% Logistic model Year Predicted Relative error population 2001 2710.0 2.76% 2002 2714.0 2.44% 2003 2729.0 2.65% 2004 2733.0 2.67% 2005 2788.0 4.44% 2006 2790.0 4.12% 2007 280h.0 4.00% 2008 2819.0 4.00% 2009 2822.0 3.77% 2010 2835.0 4.08%
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|Publication:||Advances in Natural Science|
|Date:||Dec 31, 2012|
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