Clarifying Chaos: A Look Into Chaotic Dynamical Systems

Dynamical systems, even simple ones, can be unpredictable. These unpredictable dynamical systems are known as chaotic dynamical systems which display irregular, complex behavior. Chaotic behavior is presented in discrete dynamical systems. More specifically, it is examined in regards to the simple system formed from the iteration of the quadratic function. A glimpse at chaotic continuous dynamical systems is provided with an examination of the Lorenz system of equations. By looking in depth at these chaotic dynamical systems, an understanding of their characteristics, properties, and capabilities is developed