Nonlinear System Visualization Using Performance Maps

J.J. Alpigini

Keywords

Visualization, performance maps, fractal dimension, chaos, simulation, nonlinear dynamics

Abstract

This research explores a visualization technique, titled the performance map, that is derived from the Julia set common in the visualization of iterative chaotic formulae. Performance maps are generated via digital computation and require a minimum of a priori knowledge of the system under evaluation. By the use of colour-coding, they convey a wealth of information to the informed user about dynamic behaviours of a system that may be hidden from all but the expert analyst. To demonstrate the effectiveness of the performance map technique, visualizations of the Duffing oscillator are presented. In visualizing the Duffing oscillator, a new fractal measurement is employed, termed the effective information dimension.

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