Function: calc[AutonomSys] - solves a general autonomous system 

Calling Sequence:  

AutonomSys(f, g, s, L, C)
AutonomSys(f, g, s, L, C, P)
Parameters:  

f, g - expressions in and  

L, C -  any names
s - stepsize
P - list of ranges related to extra critical points:  

Description: 

• AutonomSys solves the general autonomous system plots the phase plane. The  linearized system is returned in L. Classification and a plot of a critical point including direction field and solution curves in the neighborhood of the point are returned in . If the direction field shows other critical points, these can be found and classified using the sixth argument P

Examples: 

>	restart: with(calc):

 

> f:=x(t)-1/10*x(t)^2-1/10*x(t)*y(t): g:=3*y(t)-1/2*y(t)^2-1/10*x(t)*y(t):   > AutonomSys(f,g,0.05,lin,C);     > C(1);     > lin[1];     > C(2);     > lin[2];

> C(3);     > lin[3];     > C(4);     > lin[4];