As this series cover from low-dimensional to high-dimensional, from linear to nonlinear, a continuous system is finally capable of generating and we finally have enough background knowledge to talk about chaos.

Non linear systems' differences from linear systems, phase portraits, and attractors.

Because high-dimensional space is difficult to understand intuitively (von Neumann and his sister&#58 we don’t), high-dimensional dynamics generally discusses linear systems first, and then regards the effects of nonlinearity as distortions of linear systems.

Phase portraits are often used to describe the qualitative and semi-quantitative behavior of dynamical systems, such as stationary points and their stability.

The ultimate goal of dynamics is to give a function of the physical quantity of interest changing with time, where time is at least one of the independent variables of this function.