Developments in Advanced Complexity Theory

The essay or review below describes or analyses the content, style and merit of the developments in Advanced Complexity Theory. Complex, self-organising, adaptive systems possess a kind of dynamism that makes them qualitatively different from static objects such as computer chips. Complex systems are more spontaneous, more disorderly, more alive than that. In the past three decades, chaos theory has shaken science to its foundations with the realisation that very simple dynamical systems can give rise to extraordinarily intricate behaviour. Chaos theory is the qualitative study of unstable, aperiodic behaviour in deterministic, non-linear, dynamical systems.Chaos / complexity scientists have identified a number of describing features of complex nonlinear systems. The main features of complex nonlinear systems are known to be “dynamic, nonlinear, chaotic, unpredictable, sensitive to initial conditions, open, self-organizing, feedback sensitive and adaptive”. Two central aspects of chaos theory are the mathematical study of abstract dynamical systems and the application of these dynamical models to complex behaviour in actual experimental systems.There are three aspects of Chaos that relate to fractal patterns, bounded infinity, and unpredictability. Since the notions of nonlinearity incorporate both chaos theory in mathematics and complexity theory in science, an understanding of complexity theory might assist in the elucidation of chaotic concepts.