Comparative Study of Chaotic and Stochastic Systems in Nature

Abstract

In this article we will seek to analyze applications of chaotic systems and stochastic systems in nature, with the purpose of carrying out a comparative study. The work begins with an exposition of the theoretical foundations of the damped oscillator, a case of chaotic system, listing three types of damping. Subsequently, Paul Langevin’s approach to Brownian motion, a case of a stochastic system, is discussed. Therefore, the behaviors of an oscillator subjected to different types of damping are exposed and compared. Finally, the stochastic behavior of a Brownian particle will be presented. The results reveal that in deterministic chaotic systems the equations of motion can be found as long as the initial conditions are known, while in stochastic systems, the presence of random terms makes an exact calculation of the equations of motion impossible, and only one can be obtained. expected value, that is, an average value of all possible states. In this article, the application of chaotic systems and stochastic systems will be presented, with the purpose to develop a comparative study. This paper begins by presenting the theoretical foundations of the damped oscillator, a case of chaotic system, listing three kinds of damping. Subsequently, Paul Langevin’s approach to the Brownian move30 ment, a case of stochastic system, will be discussed. Consequently, the behaviors of an oscillator under different kinds of damping will be presented and compared. Lastly, the stochastic behavior of a Brownian particle will be presented.