A numerical study of coupled maps representing energy exchange processes between two environmental interfaces regarded as biophysical complex systems

Abstract

The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.