Could someone suggest me an easy guide to transforming a system of differential equations into normal form around a particular point? As I understand, normal forms are used in border collision bifurcations to define the new set of coordinates around the parameter value [itex]\mu _0[/itex]. By doing this, we accomplish finding the trajectory of the solution curve in the new half of the plane, am I right? (assuming our state space is divided into 2 halves) I also came across normal forms while reading-up on a paper-'Generating Chaos in Continuous-Time Systems via Feedback Control' by Wang. I am still trying to understand the connection between normal forms and chaotification. If someone has any idea, this also would be very helpful.