Understanding the complexity in low dimensional systems

Abstract

Complex System is any system that presents involved behavior, and is hard to be modeled by using the reductionist approach of successive subdivision, searching for ''elementary'' constituents. Nature provides us with plenty of examples of these systems, in fields as diverse as biology, chemistry, geology, physics, and fluid mechanics, and engineering. What happens, in general, is that for these systems we have a situation where a large number of both attracting and unstable chaotic sets coexist. As a result, we can have a rich and varied dynamical behavior, where many competing behaviors coexist. In this work, we present and discuss simple mechanical systems that are nice paradigms of Complex System, when they are subjected to random external noise. We argue that systems with few degrees of freedom can present the same complex behavior under quite general conditions