Entropy in Dynamic Systems

Abstract

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor and control complicated chaotic and stochastic processes [...]

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

“…In recent years, fractional stochastic partial differential equations (FSPDEs) have risen to the forefront of mathematical innovation, owing to their sophisticated approach to depicting the dynamics of processes that are often oversimplified by conventional mathematical models [29]. FSPDEs provide the mathematical community with a powerful toolkit to investigate, model, and address problems that involve not only randomness and extensive interactions but also memory effects.…”

Analyzing Double Pendulum Dynamics with Approximate Entropy and Maximal Lyapunov Exponent

“…This measurement is based on the uncertainty correlated to a variable's probability [15]. Signal entropy uses the same reasoning but measures the information in a discrete time signal [2,4,14]. A periodic signal would have less information because there is less uncertainty in the signal [2,4].…”

“…Signal entropy uses the same reasoning but measures the information in a discrete time signal [2,4,14]. A periodic signal would have less information because there is less uncertainty in the signal [2,4]. Therefore, signal entropy is an objective measurement of a discrete time signal periodicity [2,4,7,14,18].…”

“…A periodic signal would have less information because there is less uncertainty in the signal [2,4]. Therefore, signal entropy is an objective measurement of a discrete time signal periodicity [2,4,7,14,18].…”