Coupled maps serving the exchange processes on the environmental interfaces regarded as complex systems

Dragutin T. Mihailovic, Mirko Budincevic, Igor Balaz, Sinisa Crvenkovic, Ilija Arsenic

Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia.
Department of Physics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia.
Faculty of Agriculture, University of Novi Sad, Novi Sad, Serbia.

DOI: 10.4236/ns.2012.48076                

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.

Keywords

Coupled Maps; Environmental Interface; Diffusive Coupling; Internal Coupling; Map with Diffusive Coupling; Map with Internal Affinity; Category Theory; Formal Concept Analysis; Chaos; Complexity; Logistic Equation; Cross Sample Entropy; Permutation Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

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