Autonomous System 

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 x(t) and y(t)  

L, C -  any names
s - stepsize
P - list of ranges related to extra critical points: [[x = x[1] .. x[2], y = y[1] .. y[2]], () .. (), [x = x[k] .. x[k], y = y[k] .. y[k]]] 

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 C(i), i = 1, 2, () .. (). 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);
 

Plot_2d
 

> C(1);
 

Plot_2d
 

> lin[1];
 

Vector[column](%id = 164911668) = Vector[column](%id = 164911732)
 

> C(2);
 

Plot_2d
 

> lin[2];
 

Vector[column](%id = 189333336) = Vector[column](%id = 189333400)
 

> C(3);
 

Plot_2d
 

> lin[3];
 

Vector[column](%id = 205734160) = Vector[column](%id = 205734224)
 

> C(4);
 

Plot_2d
 

> lin[4];
 

Vector[column](%id = 152892684) = Vector[column](%id = 152870952)