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Revision difference : autonomous system
Version 2 Version 1
A system of ordinary differential equation is \emph{autonomous} when it does not depend on time \textit{(does not depend on the independent variable)} i.e. $\dot{x}=f(x)$. In contrast \emph{nonautonomous} is when the system of ordinary differential equation does depend on time \textit{(does depend on the independent variable)} i.e. $\dot{x}=f(x,t)$.\\ A system of ordinary differential equation is \emph{autonomous} when it does not depend on time \textit{(does not depend on the independent variable)} i.e. $\dot{x}=f(x)$. In contrast \emph{nonautonomous} is when the system of ordinary differential equation does depend on time \textit{(does depend on the independent variable)} i.e. $\dot{x}=f(x,t)$.\\
It can be noted that every nonautonomous system can be converted to an autonomous system by additng a dimension. i.e. If $\dot{\textbb{x}}=\textbb{f}(\textbb{x},t)$ $\textbb{x} \in \mathbb{R}^n$ then it can be written as an autonomous system with $\textbb{x} \in \mathbb{R}^{n+1}$ and by doing a substitution with $x_{n+1} = t$ and $\dot{x}_{n+1}=1$.
It can be noted that every nonautonomous system can be converted to an autonomous system by additng a dimension. i.e. If $\dot{\textbf{x}}=\textbf{f}(\textbf{x},t)$ $\textbf{x} \in \mathbb{R}^n$ then it can be written as an autonomous system with $\textbf{x} \in \mathbb{R}^{n+1}$ and by doing a substitution with $x_{n+1} = t$ and $\dot{x}_{n+1}=1$.