1. Could someone explain me what is the fundamental difference between the dynamical system of the kind $\dot x = f(x)$ and $E \dot x= f(x)$ where $E$ is an matrix with real entries. For the first system, a state is $x(t)$ at time $t$; is it the same for the second system? I wish to visualise trajectories of such type of dynamical system to be more precise.

  2. Consider a continuous time dynamical system \begin{align} \dot x= f\left(x\right) \end{align} on a state-space $\mathcal{X}$, where $x$ is a coordinate vector of the state, $f$ is a non-linear vector valued smooth function of the same dimension as its argument $x$.

    Could anyone tell me why assume $f$ to be smooth and what it means by ''function of the same dimension as its argument $x$'', what is a dimension of function, by the way, and why its dimension needs to be equal as $x$?

Thank you for your clarification.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.