📂Dynamical Systems

Open Dynamical Systems and Stationarity

Definition ^{1 2}

1. If there exist external factors $\lambda$ that influence the system $\dot{x} = f (x)$ and can change the fate of a trajectory, the system is called an open system.
2. If an open system is independent of time $t$, it is called stationary; if it depends on time as in $\dot{x} = f \left( x , \lambda (t) \right)$ and satisfies $\lambda = \lambda (t)$, it is called non-stationary.

Explanation

In stationary systems, the dynamical changes that occur as parameters vary are called bifurcations, whereas the dynamical changes that occur in non-stationary systems are called tipping points.