NS  Vol.4 No.8 , August 2012
Coupled maps serving the exchange processes on the environmental interfaces regarded as complex systems
ABSTRACT
We have defined the environmental interface through the exchange processes between media forming this interface. Considering the environmental interface as a complex system we elaborated the advanced mathematical tools for its modelling. We have suggested two coupled maps serving the exchange processes on the environmental interfaces spatially ranged from cellular to planetary level, i.e. 1) the map with diffusive coupling for energy exchange simulation and 2) the map with affinity, which is suitable for matter exchange processes at the cellular level. We have performed the dynamical analysis of the coupled maps using the Lyapunov exponent, cross sample as well as the permutation entropy in dependence on different map parameters. Finally, we discussed the map with affinity, which shows some features making it a promising toll in simulation of exchange processes on the environmental interface at the cellular level.

Cite this paper
Mihailovic, D. , Budincevic, M. , Balaz, I. , Crvenkovic, S. and Arsenic, I. (2012) Coupled maps serving the exchange processes on the environmental interfaces regarded as complex systems. Natural Science, 4, 569-580. doi: 10.4236/ns.2012.48076.
References
[1]   Gladwell, M. (2000) The tipping point: How little things can make a big difference, first edition. Little Brown, London.

[2]   Paola, C. and Leeder, M. (2011) Environmental dynamics: Simplicity versus complexity. Nature, 469, 38-39. doi:10.1038/469038a

[3]   Sizykh, A.P. (2007) Plant communities of environmental interfaces as a problem of ecology and biogeography. Biollogy Bulletin, 34, 292-296. doi:10.1134/S1062359007030120

[4]   Lehtonen, M. (2004) The environmental-social interface of sustainable development: Capabilities, social capital, institution. Ecological Economics, 49, 199-214. doi:10.1016/j.ecolecon.2004.03.019

[5]   Rasmussen, K. and Arler, F. (2010) Interdisciplinarity at the human-environment interface. Danish Journal of Geography, 110, 37-45.

[6]   Banks, J., Carson, J.S., Nelson, B.L. and Nicol, D.M. (2009) Discrete-event system simulation. Prentice Hall, Upper Saddle River.

[7]   Mihailovic, D.T. and Balaz, I. (2007) An essay about modeling problems of complex systems in environmental fluid mechanics. Idojaras, 111, 209-220.

[8]   Mihailovic, D.T., Budincevic, M., Perisic, D. and Balaz, I. (2012) Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise. Chaos, Solitons & Fractals, 45, 156-165. doi:10.1016/j.chaos.2011.11.005

[9]   Duffy, D.M., Harding, J.H. and Stoneham, A.M. (1992) Atomistic modeling of the metal/oxide interface with image interactions. Acta Metallurgica et Materialia, 40, 11-16. doi:10.1016/0956-7151(92)90258-G

[10]   Mihailovic, D.T., Budincevic, M., Balaz, I. and Mihailovic, A. (2011) Stability of intercellular exchange of biochemical substances affected by variability of environmental parameters. Modern Physics Letters B, 25, 2407-2417. doi:10.1142/S0217984911027431

[11]   Neofytou, P., Venetsanos, A.G., Vlachogiannis, D., Bartzis, J.G. and Scaperdas, A. (2006) CFD simulations of the wind environment around an airport terminal building. Environmental Modelling & Software, 21, 520- 524. doi:10.1016/j.envsoft.2004.08.011

[12]   Lloyd, A.L. (1995) The coupled logistic map: A simple model for effects of spatial heterogeneity on population dynamics. Journal of Theoretical Biology, 173, 217-230. doi:10.1006/jtbi.1995.0058

[13]   Mihailovic, D.T., Budincevic, M., Kapor, D., Balaz, I. and Perisic, D. (2011) A numerical study of coupled maps representing energy exchange processes between two environmental interfaces regarded as biophysical complex systems. Natural Science, 1, 75-84.

[14]   Behrens, T.M., Dix, J. and Hindriks, K.V. (2009) Towards an environment interface standard for agent-oriented programming. Technical Report IfI-09-09, Clausthal University of Technology.

[15]   Serletis, A., Shahmoradi, A. and Serletis, D. (2007) Effect of noise on the bifurcation behavior of nonlinear dynamical systems. Chaos, Solitons & Fractals, 33, 914-921. doi:10.1016/j.chaos.2006.01.046

[16]   Serletis, A., Shahmoradi, A. and Serletis, D. (2007) Effect of noise on estimation Lyapunov exponents from a time series. Chaos, Solitons & Fractals, 32, 883-887. doi:10.1016/j.chaos.2005.11.048

[17]   Serletis, A. and Shahmoradi, A. (2006) Comment on ‘‘Singularity Bifurcations’’ by Yijun He and William A. Barnett. Journal of Macroeconomics, 28, 23-26. doi:10.1016/j.jmacro.2005.10.002

[18]   Savi, M.A. (2007) Effects of randomness on chaos and order of coupled maps. Physical Letters A, 364, 389-395. doi:10.1016/j.physleta.2006.11.095

[19]   Liu, Z., Ma, W. (2005) Noise induced destruction of zero Lyapunov exponent in coupled chaotic systems. Physical Letters A, 343, 300-305. doi:10.1016/j.physleta.2005.06.044

[20]   Rosen R. (1991) Life itself, a comprehensive inquiry into the nature, origin, and fabrication of life. Columbia University Press.

[21]   Mesarovic, M. and Takahara, Y. (1972) General systems theory: Mathematical foundations. Academic Press, Inc., London.

[22]   Wille, R. (1982) Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I., Ed., Ordered Sets: Proceedings. NATO Advanced Studies Institute, 83, Reidel, Dordrecht, 445-470.

[23]   Ganter, B. and Wille, R. (1997) Formal concept analysis: Mathematical foundations. Springer-Verlag, Berlin.

[24]   Levich, A.P., Solov’yov, A.V. (1999) Category-functor modeling of natural systems. Cybernetics and Systems, 30, 571-585. doi:10.1080/019697299125118

[25]   Checkland, P.B. (1981) Systems thinking, systems prac- tice. Wiley, New York.

[26]   Klir, G.J. (2002) The role of anticipation in intelligent systems. In: Dubois, D.M., Ed., Computing Anticipatory Systems (CASYS’01), 627, pp. 37-46.

[27]   Rossiter, N. and Heather, M. (2005) Conditions for interoperability. 7th International Conference of Enterprise Information Systems (ICEIS), Florida, 92.

[28]   Bell, J.S. (1964) On the Einstein Podolsky Rosen paradox. Physics, 1, 195-200.

[29]   Manes, E.G. and Arbib, M.A. (1975) Arrows, structures and functors, the categorical imperative. Academic Press.

[30]   Wolkenhauer, O. and Hofmeyr, J.-H. (2007) An abstract cell model that describes the self-organization of cell function in living systems. Journal of Theoretical Biology, 246, 461-476. doi:10.1016/j.jtbi.2007.01.005

[31]   Vandermeer, J., Stone, L. and Blasius, B. (2001) Categories of chaos and fractal basin boundaries in forced predator-prey models. Chaos, Solitons & Fractals, 12, 265-276. doi:10.1016/S0960-0779(00)00111-9

[32]   Engel, A., Szidarovszky, F. and Chiarella, C.A. (2003) Game theoretical partially cooperative model of inter- national fishing with time delay. Chaos, Solitons & Fractals, 18, 549-560. doi:10.1016/S0960-0779(02)00676-8

[33]   Chiarella, C.F. and Szidarovszky, F. (2003) Bounded continuously distributed delays in dynamic oligopolies. Chaos, Solitons & Fractals, 18, 977-993. doi:10.1016/S0960-0779(03)00067-5

[34]   Devaney, R.L. (2003) An introduction to chaotic dynamical systems. Westview Press, Colorado.

[35]   Gunji, Y.-P. and Kamiura, M. (2004) Observational heterarchy enhancing active coupling. Physica D, 198, 74-105. doi:10.1016/j.physd.2004.08.021

[36]   Ullner, E., Koseska, A., Kurths, J., Volkov, E., Kantz, H. and Ojalvo, J.G. (2008) Multistability of synthetic genetic networks with repressive cell-to-cell communication. Physical Review E, 78, 031904. doi:10.1103/PhysRevE.78.031904

[37]   Barkai, N. and Shilo, B.Z. (2007) Variability and robustness in biomolecular systems. Molecular Cell, 28, 755- 760. doi:10.1016/j.molcel.2007.11.013

[38]   Heagy, J.F., Platt, N. and Hammel, S.M. (1994) Characterization of on-off intermittency. Physical Review E, 49, 1140. doi:10.1103/PhysRevE.49.1140

[39]   Metta, S., Provenzale, A. and Spiegel, E.A. (2010) On-off intermittency and coherent bursting in stochastically-driven coupled maps. Chaos, Solitons & Fractals, 43, 8-14. doi:10.1016/j.chaos.2010.06.001

[40]   Furstenberg, H. and Kesten, H. (1960) Products of random matrices. The Annals of Mathematical Statistics, 40, 457-469. doi:10.1214/aoms/1177705909

[41]   Fischer-Friedricha, E., Meacci, G., Lutkenhausc, J., Chatéd, H. and Krusee, K. (2010) Intra- and intercellular fluctuations in Min-proteindynamics decrease with cell length. Proceedings of the National Academy of Sciences, USA, 107, 6134-6139. doi:10.1073/pnas.0911708107

[42]   Howard, M. and Ruten-berg, A.D. (2003) Pattern formation inside bacteria: Fluctuations due to the low copy number of proteins. Physical Review Letters, 90, 128102. doi:10.1103/PhysRevLett.90.128102

[43]   Pincus, S. and Singer, B.H. (1995) Randomness and degrees of irregularity. Proceedings of the National Academy of Sciences, USA, 93, 2083-2088. doi:10.1073/pnas.93.5.2083

[44]   Pincus, S.M., Mulligan, T., Iranmanesh, A., Gheorghiu, S., Godschalk, M. and Veldhuis, J.D. (1996) Older males secrete luteinizing hormone and testosterone more irregularly, and jointly more asynchronously, than younger males. Proceedings of the National Academy of Sciences, USA, 93, 14100-14105. doi:10.1073/pnas.93.24.14100

[45]   Bandt, C., Pompe, B. (2002) Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88, 174102. doi:10.1103/PhysRevLett.88.174102

[46]   Boschetti, F. (2007) Mapping the complexity of ecological models. Ecological Complexity, 5, 37. doi:10.1016/j.ecocom.2007.09.002

[47]   Arshinov, V. and Fuchs, C. (2003) Preface. In: Arshinov, V. and Fuchs, C., Eds., Causality, Emergence, Self-Organisation, NIA-Priroda, Moscow, 1-18.

 
 
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