Kolmogorov complexity and chaotic phenomenon in computing the environmental interface temperature

Abstract

In this paper, we consider the chaotic phenomenon and Kolomogorov complexity in computing the environmental interface temperature. First, the environmental interface is defined in the context of the complex system, in particular for autonomous dynamical systems. Then we consider the following issues in modeling procedure: (i) how to replace given differential equations by appropriate difference equations in modeling of phenomena in the environmental world? (ii) whether a mathematically correct solution to the corresponding differential equation or system of equations is always physically possible and (iii) phenomenon of chaos in autonomous dynamical systems in environmental problems, in particular in solving the energy balance equation to calculate environmental interface temperature. The difference form of this equation for computing the environmental interface temperature is discussed and analyzed depending on parameters of equation, using the Lyapunov exponent and sample entropy. Finally, the Kolmogorov complexity of time series obtained from this difference equation is analyzed. © 2012 World Scientific Publishing Company.