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.

Chaos in Computing the Environmental Interface Temperature: Nonlinear Dynamic and Complexity Analysis of Solutions

“…Because of Eq. ( 15) has form of logistic map we know that chaos is present in a case when logistic parameter r is in interval [3,4] so parameter of coupling ε should be very small, i.e. beyond 0.1.…”

“…2 There are a lot of examples of environmental interfaces in the nature such as interface between cells, human or animal bodies and surrounding environment, aquatic species and water around them and natural or artificially created surfaces and atmosphere. 3 A typical example of environmental interface in the nature is the ground surface, where exists all three mechanisms of energy transfer; incoming and outgoing radiation, convection of heat and moisture into the atmosphere and conduction of heat into deeper soil layers of ground. 4 Parameterization of these processes is of great importance for environmental models of different spatial and temporal scales.…”