ISSN 1749-3889 (print), 1749-3897 (online)
International Journal of Nonlinear Science
Vol.14(2012) No.3,pp.375-378
A New Type of Air-Soil-Land Plant Carbon Cycle System
Min Fu ∗ , Lixin Tian, Guochang Fang
Energy Development and Environmental Protection Strategy Research Center,Jiangsu University,
Zhenjiang,Jiangsu,212013,PR China
(Received 28 June 2012 , accepted 26 October 2012)
Abstract: The paper is focused on a kind of new dynamic evolution of ASP carbon cycle system, which is
established on the complex interrelation of carbon cycle amoung air, soil, land plants. In this paper, model
establishment is explicitly introduced and the dynamic behavior of the system is substantially analyzed.
Keywords:Carbon cycle; air; soil; land plant
1
Introduction
The research of carbon cycle system can show clearly the carbon exchange between different spheres on the earth , its
impact so as to probe the interaction of the different systems on the earth and the influence of human being’s activities.
Researches on carbon cycle have been one of the hot topics.
Goudie and other researchers[1] have studied the impact of weather on the global carbon cycle , especially the dynamic
relation and erosion ,which will contribute to the carbon cycle research. Strohbach and his team[2] studied how the urban
green space works in the global carbon cycle. His research shows urban green space as carbon sink, if designed and
maintained well, may have a strong impact on the carbon footprint. Nakata and other researchers[3] studied a physical–
biological coupled ocean carbon cycle model and made a primary analysis of their research findings’ trend. Dasgupta and
others[4] worked on the deep carbon cycle in Earth’s interior. Liu Chunying and his team[5] researched the change in
organic carbon storage in soil and its spatial distribution in China wetlands in different climatic regions. His conclusion is
significant in indicating the characteristics of organic carbon storage in wet land soil and its interrelations with the carbon
cycle in the ecological system on the land. And his research also helps evaluate and protect the ecological system in the
wet lands. Leng Fangwei and others[6] made a review on the recent progress in carbon cycle research in East Asia. Fan
Yuejun and others[7] probed the effect of global warming on the carbon cycle on the grassland ecosystems after reviewing
the relevant researches and also pointed out the exiting problems in the researches on carbon cycle on the grasslands and
suggested the direction of future researches.
Chaotic analysis and its application in the dynamic evolutionary system begin to work practically in engineering,
biology and economy[8-9]. Carbon cycle system is a complex system characteristic of complex coupling, time lag and
non-linearity. The system includes air, soil (wet land, grassland and etc.), land animal, land plant, river, ocean[10-11]
and deep carbon cycle in the Earth’s interior[12]. What’s eye-catching now is how to study carbon cycle using non linear
dynamics, however, the exiting researches focused on scenario analysis ,which is not so satisfactory because of no specific
carbon cycle model available, too many uncertainty factors in research data and vague regular patterns of carbon cycle.
The paper is trying to establish ASP carbon cycle model, a nonlinear evolutionary model of carbon cycle based on the
complex interrelations between air, soil and land plant (ASP). The evolutionary regular patterns between variables will be
systematically analyzed with non linear dynamics.
The paper is organized as follows. The model is set up in Section 2. Section 3 analyse the basic properties of the ASP
carbon cycle system. Conclusions are finally presented in Section 4.
2
Establishment of model
Beginning with terrestrial carbon cycle, many researchers studied the carbon cycle in the ecosystems such as wet land,
marsh, grassland and etc. They also took the ocean into carbon cycle system, thus a broader carbon cycle system including
∗ Corresponding
author.
E-mail address: [email protected]
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International Journal of Nonlinear Science, Vol.14(2012), No.3, pp. 375-378
oceans developed. Some of the researchers further studied the deep carbon cycle in the earth interior. Generally speaking,
the research trend is to combine biological issues with bigger terrestrial physical issues such as air, ocean, lithosphere,
sun-earth space and etc, in a hope for a comprehensive study of carbon cycle and combination with other dynamic process.
The paper, based on the complex recycling evolution between air, soil and land plant in certain period and scale, deduces
the ASP carbon cycle system as follows:

 ẋ = p1 − q1 x (x/A − 1) + a21 y − a12 x + a31 z − b13 xz
ẏ = p2 − q2 y + a12 x − a21 y + a32 z
(1)

ż = b13 xz − a31 z − a32 z
where x (t)is the carbon storage changeable with time in air in certain range; y (t)is the one in soil; z (t) is the one in land
animal. pi ,qi ,ajk ,bjk ,Aare positive constants, t ∈ I, I is the economy period (i = 1, 2,j = 1, 2, 3,,k = 1, 2, 3, )
p1 is the increased carbon amount into x (t) for airflow and other reasons; −q1 x (x/A − 1) is the reduced carbon
amount in x (t); A, the peak value; a21 y, increased carbon amount in x (t) for soil breathing, air flowing and etc with
a21 as the coefficient; −a12 x, the precipitated carbon into y (t) from x (t) with a12 as the coefficient; a31 z, the discharged
carbon into x (t) from z (t) for burning or breathing; In formula (1), the first equation indicates: variance rate of carbon
storage in x (t) is relevant both to carbon input and output in x (t) of carbon cycle system and to carbon exchange between
y (t), z (t) ; as for −q1 x (x/A − 1), when x < A,namely, x/A − 1 < 0, it shows that the carbon level in air is not saturate
and carbon reduces slowly with small or no output; when x > A,namely, x/A − 1 > 0, it shows that the carbon level in
air is saturate and carbon reduces quickly with great output. Recyclable evolutionary process is shown in figure 1.
p2 is the input carbon into y (t) for rivers’ scouring and scrubbing. −q2 y is the carbon output from y (t) with q2 as
coefficient. a12 x is the carbon precipitated into y (t) from x (t). −a21 y is the discharged carbon from y (t) into x (t).
a32 z is discharged carbon from z (t) into y (t) for land plant’respiration and dead bodies’decomposition with a32 as the
coefficient. The second equation in the first formula shows variance rate of carbon storage in y (t) is relevant both to
carbon input and output in y (t) of carbon cycle system and to carbon exchange between x (t), z (t).
b13 xz is the transmitted carbon from x (t) to z (t) with b13 as the transmission coefficient.a31 z is the discharged
carbon into x (t) for burning and breathing while a32 z is the one into y (t) for land plant respiration and dead bodies’decomposition. The third equation in the formula indicates the variance rate of carbon storage in z (t) is relevant to its
own development and the carbon exchange between x (t), y (t) .
Figure 1: carbon cycle evolution
3
Dynamic analysis
System (1) is a fairly complex one of dynamic evolution. When pi ,qi ,ajk ,bjk ,A take different figures, it will show different
dynamic behavior. For example, when system (1) takes the figures as shown in formula (2), it turns out to have a stable
solution. Figure2 shows the three-dimensional phase and time series figure when it takes such coefficient as follows.
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M. Fu, L. Tian, G. Fang: A New Type of Air-Soil-Land Plant Carbon Cycle System
377
p1 = 0.15, q1 = 0.134, a21 = 0.59, a12 = 0.485, a31 = 0.018,
b13 = 0.22, p2 = 0.25, q2 = 0.072, a32 = 0.085, A = 2.9.
(2)
Formula (1) has three equilibrium points
S1 (−2.0942, −1.1566, 0) , S2 (3.8526, 3.2002, 0) , S3 (0.4682, 6.2862, 43.3460)
After calculation, the eigenvalues of the Jacobian matrix-a linear approximation system- at each equilibrium point
are as follows: the ones at S1 are λ1 = 0.1817, λ2 = −1.0012, λ3 = −0.5637; the ones at S2, λ1 = −1.2199, λ2 =
−0.1491, λ3 = −0.7446; the ones at S3, λ1 = −9.8741, λ2 = −0.0083, λ3 = −0.7100; Therefore, S1 ,S2 are all saddle
points while S3 is the stable point.
ASP is a new carbon cycle system, which reflects the real interrelation between variables. Thus, ASP system has
ampler theory evidences, which is closer to reality and has more popular application than other carbon cycle theories.
Figure 2:
4
(a) three-dimensional phase diagram
(b) Times series figure
Conclusion
The paper brings air, soil, land plant into a nonlinear dynamic evolution model, which explicitly expresses how ASP,
the carbon cycle dynamic evolution model, is established. With nonlinear dynamics, the author analyzed the dynamic
behavior of ASP carbon cycle system, which is a complex nonlinear system characteristic of coupling, time lag and
nonlinearity. For the special structure of ASP system, current research findings indicate that in most cases, the system is
stable, and the phase diagram and time series plot are also available in the paper.
Acknowledgements
The research is supported by the Major Program of the National Social Science Foundation of China (Nos. 12&ZD062),
the National Natural Science Foundation of China (Nos. 71073072 and 51276081), Doctoral Fund of Ministry of Education of China (No. 20093227110012 and No.1201190070), Natural Science Foundation of Jiangsu (No. BK2010329), and
Natural Science Foundation of the Jiangsu Higher Education Institutions (No. CXLX11 0589).Soft Science Foundation
of Jiangsu Province (No. BR 2012027).
References
[1] Goudie AS, Viles HA. Weathering and the global carbon cycle. Geomorphological perspectives. Earth-Science Reviews , 113(2012): 59–71.
[2] Strohbacha MW, Arnold E, Haase D. The carbon footprint of urban green space—A life cycle approach. Landscape
and Urban Planning, 104(2012): 220– 229.
IJNS homepage: http://www.nonlinearscience.org.uk/
378
International Journal of Nonlinear Science, Vol.14(2012), No.3, pp. 375-378
[3] Nakata K, Doi T. Estimation of primary production in the ocean using a physical–biological coupled ocean carbon
cycle model. Environmental Modelling & Software,21(2006): 204–228.
[4] Dasgupta R, Hirschmann MM. The deep carbon cycle and melting in Earth’s interior. Earth and Planetary Science
Letters,298(2010): 1–13.
[5] Liu CY , Zhou WB. Progress of Research on Carbon Cycle of Wetlands in China. Chinese Journal of Soil Science,
43(5)(2012):1464–1270 (in Chinese).
[6] Leng FW. The Recent Progress of Carbon Cycle Research in East Asian. Progress in Biochemistry and Biophysics ,
38(11)(2011): 1015–1019 (in Chinese).
[7] Fan YJ, Hou XY, Shi HX, Shi S. Effect of carbon cycling in grassland ecosystems on climate warming. Acta Prataculturae Sinica ,21(3)(2012): 294-302 (in Chinese).
[8] Tian LX, Jin RL. Theoretical exploration of carbon emissions dynamic evolutionary system and evolutionary scenario analysis. Energy ,40(2012): 376–386.
[9] Fang GC, Tian LX, Sun M, Fu M. Analysis and application of a novel three-dimensional energy-saving and emissionreduction dynamic evolution system. Energy,40(2012): 291–299.
[10] Woloszyn M, Mazloff M, Ito T. Testing an eddy-permitting model of the Southern Ocean carbon cycle against
observations. Ocean Modelling ,39(2011):170–182.
[11] Menviel L, Joos F, Ritz SP. Simulating atmospheric co2 , 13 C and the marine carbon cycle during the Last GlacialeInterglacial cycle: possible role for a deepening of the mean remineralization depth and an increase in the oceanic
nutrient inventory. Quaternary Science Reviews,56(2012): 46–68.
[12] Zhang HM, Li SG. Deep carbon recycling and isotope tracing: Review and prospect. Science China
Press,42(10)(2012): 1459 –1472 (in Chinese).
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