Nonlinear dynamics

Apparently stochastic, erratic behavior of a deterministic simulation model, describing the convection in the atmosphere by a system of three coupled nonlinear differential equations, led to the fall of the world view that was based on strong causality. During the past three decades, new terms like chaotic attractor , bifurcation, and fractals emerged together with the hope to understand and describe complex phenomena by means of small-scale models.

Whereas there have to be at least three interacting variables in the case of continuous-time systems for such phenomena to arise, in discrete systems one variable is sufficient. Due to this fact, in our opinion students of computer science should get the opportunity to learn about these aspects.

One consequence of the new world view is the distinction between weak and strong causality. Weak causality means that same causes are followed by same consequences, and strong causality means that similar causes are followed by similar consequences. Today, it has to be accepted that even deterministic systems do not always react in a strongly causal way. Although deterministic chaotic trajectories may locally diverge in time and phase space, there can exist complex order in strange attractors. This order can be characterized by non-integer valued (fractal) dimensions or corresponding Rényi entropies, and often simple nonlinear models can be found that produce the observed complex behavior.

Practical applications of the relatively new field of research called nonlinear dynamics are investigated together with engineers and other scientists.