Hi there, I'm new to this but I was wondering if you could help me with my understanding of Dynamical Systems.
I have a continuous dynamical system given by the equations:
dx1/dt = x1(x2-x3)
dx2/dt = x2(x3-x1)
dx3/dt = x3(x1-x3)
Which I need to analyse. There are a few problems I have but the main ones are centred around orbits.
My question is why can an orbit starting in the region x1 >= 0, x2 >= 0 , x3 >= 0 never cross one of the lines x_i = 0?
Any help on the matter would be greatly appreciated I'm drawing a complete blank with this and could really do with some help.