Fuzzy Differential Equations as a Tool for Teaching Uncertainty in Engineering and Science

Abstract

This paper presents fuzzy differential equations in the context of teaching uncertainty in engineering and science. Moreover, the Cauchy problem is discussed as case of study to understand the importance of fuzzy differential equations as a natural way to model uncertainty in dynamical systems. The specific case of study reported in this paper is the Malthusian population dynamic model, which is solved by students both via analytical as well as computational approaches as a result of applying problem-based learning teaching principles, and allowing to introduce the importance of uncertainty.

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

“…Besides properties such as the existence and topology of fixed points and dynamics' time variability, some other features have grabbed researchers' attention. Oscillators with time delays in their equations [13], fractional equations [14], fuzzy differential equations [15], those with hyperchaos [16], and others with synchronization among a group of them [17] can be examples of chaotic systems with specific features. Multistability is another of these features [18].…”

Mamdani‐Type Fuzzy‐Based Adaptive Nonhomogeneous Synchronization

“…e synchronization phenomena among dynamical systems are a widely studied topic in the last decades due to the vast amount of applications in science and engineering [1][2][3]. In the related literature, dynamical systems and synchronization applications in many fields can be found, from biology [4,5], mechanical systems [6][7][8][9], chemistry [10], physics [11,12], fuzzy modeling [13][14][15][16] to secure communications [17][18][19], among many others. In general, it is said that a set of dynamical systems achieve synchronization if trajectories in each system approach a common trajectory.…”