when we do the linearization we do transfer the critical point to the orgin, i want see the plot of nonlinear system before the linearization and after linearization which is critical point is tranfered to orgin, also i try to find `conserved quantity` and make a good plot with the critical point shown in graph how i can do the linearization by maple, also  we  by hand when we solved we show that in new system when we give him variable we have to write for each new system  u=x-x[0] when is u is new system for linearization we need that or not? becuase result is not change when we take jacobian result is same !

Linearization.mw

i want plot a system of differential equation and do phaseportrait i did but when i want make it a little bit more clear and colorfull like rainbow when i find the C.Q i don't know how set the option for ploting?

e1.mw

i have a system but i don't know how i can plot chaotic or is need time for ploting or not ?

Regarding to this equation i want to do the same as paper did, but i am not sure how i can determine the both  point in plot and how thus point show effect of system of equation and  how find jacobian in the two different point  i think he find it in general but i think we have to find it for each one  of equalibriom point  or we just find in general .
thus plot also are emazing did he use special code in matlab or mathematica? there is some app for plot thus kind of phase portrait but they not like this this is must have a special code for plotting in matlab or mathematica

Download bi-1.mw

in thus example all of them are write in shape of matrix but all of them are linear differential equation which have critical point zero ,i want to plot thus example and decided the kind of critical point by eagenvalue and by eagenvector i can find the trajectory how i can plot by matrix of each example and show that that critical point is which type as mention in picture?

system-phase-examples.mw