Visualization of controllable regions in real-time systems using a 3D-Julia set methodology

The paper introduces the possibility of the occurrence of chaos in any iterative system, and then explains how the familiar Julia set visualization can be programmed into a graphical tool. Stability on real-time systems occurs in regions of operation and is dependent on the simultaneous values of several parametric values. Because of this, it is very difficult to explore regions of instability in real, non-trivial systems. A variation of the Julia set methodology is presented, based on the corollary between the iterated fate of a function and the final value of a dynamic system. The resultant software is demonstrated on a model of a nonlinear control system, that has been reported to exhibit chaos in its feedback components-but still maintaining primary control. The paper concludes with a statement of how the visualization tool may be applied almost any (mathematically modeled) system in order to demonstrate how its dynamics can be investigated without the need for any other control analysis methods