Used frequently in 2-dimensional systems. A bifurcation in which the system switches to a new behavior with twice the period of the original system. The hallmark of this is a Floquet multiplier of -1. A sequence of period doubling bifurcations ultimately ending in chaotic behavior. A trajectory which after time , the period, comes back to its initial point.
Phase portrait A plot of two or more dynamical variables against each other.
The set of all possible initial conditions for a dynamical system. Orbit Trajectory of differential equation. A bifurcation in which a limit cycle collides with a saddle-point at a homoclinic orbit. As the bifurcation is approached, the period of the limit cycle tends to infinity as . A bifurcation in which a limit cycle collides with a saddle-node point .