Chaos theory involves the study of how perturbations in initial conditions can result in complicated behavior. Some examples of chaotic behavior are weather patterns, certain electrical networks, cardiac activity, and turbulent flow systems. One can construct relatively simple networks that exhibit, with a feedback (or feedforward) mechanism, either stable or unstable characteristics, depending upon small changes in the input.

The objective of this paper is to give graphical answers to such questions as “For what input values does chaotic behavior occur?” and “When complex signals are propagated through a signal processing network with either feedforward or feedback paths, what will the resultant output be?” The paper also presents various graphic patterns that result from chaotic behavior.

A scheme attributed to Sinanoglu for drawing networks that represent chaotic processes uses solid lines to denote the variables and wiggly lines to denote the transformation. This technique displays the inherent similarity in networks that have the same skeleton.

Numerous figures show the intricate patterns that various network topologies and processes produce. This paper provides insight into the graphic characterization of networks that display both convergent and divergent properties. For an in-depth introduction to and further information on chaos in dynamical systems, and techniques for recognizing and classifying ODE chaotic behavior, see Chua [1].