@Preben Alsholm 

Hi again. Finally I am able to produce a plot that I wanted to see (see figure below). however, I still want to make some improvements to it. I used the following code to produce it

A1:=plot([seq(Pts(beta)[1][i],i=1..4)],beta=1..1.9,color=[red,blue,green,gold],linestyle=solid,thickness=2):
A2:=plot([seq(Pts(beta)[2][i],i=1..4)],beta=1.9..4,color=[red,blue,green,gold],linestyle=longdash,thickness=2):

B1:=plot([seq(Pts(beta)[1][i],i=1..4)],beta=1.9..4,color=[red,blue,green,gold],style=point,symbol=circle):
B11:=plot([seq(Pts(beta)[1][i],i=1..4)],beta=1.6..4,color=[red,blue,green,gold], linestyle=solid,thickness=2):
plots:-display([A1,A2,B1,B11],labels=["X","Y"],font=["Times","Roman",18],labeldirections=[default,vertical],axis=[gridlines=10]);

From this image I wanned to distinguish the two equilibrium points (one with lines and one with circles and a line passing through them) and their stability (continuous part for stable, discontinuous part for unstable).

The figure looks okay on the Maple worksheet. But when I included this figure in a latex document the quality of the resulting figure is very poor. The circles (with a line passing through them) are so packed that the curve looks like a thick line.  Questions:

1) is there a way to improve the plot to make the circles more visible. I was thinking if the plot can produce circles with a greater space inbetween them, then it may help. But i don't know how to do this using plot().

PS: I do not want to remove the B11 plot.

2) Is there a better way to improve the resolution of the image. i used right-click export menu to save it as JPEG format.

Could anyone please help me to improve the plots.

thanks

Thank you. that is very helpful

Thank you. that is very helpful

Hi again,

thanks for guiding me on how to plot the equilibrium points.

However that is part of what i wanned to do.

I would like to

1)compute the eigenvalues of the jacobian of sys, evaluated at the equilibrium points given by the

procedure Pts(beta),

2) show the stability of the equilibrium points on the diagram (say stable-dashed, unstable = solid)

Any help is appreciated

Here is my modified codenonlinearsystem2.mw

cheers

A:=plot([seq(Pts(beta)[1][i],i=1..4)],beta=1..4,color=[red,blue,green,maroon]):
B:=plot([seq(Pts(beta)[2][i],i=1..4)],beta=1..4,color=[red,blue,green,maroon]):
plots:-display([A,B]);

Hi again,

thanks for guiding me on how to plot the equilibrium points.

However that is part of what i wanned to do.

I would like to

1)compute the eigenvalues of the jacobian of sys, evaluated at the equilibrium points given by the

procedure Pts(beta),

2) show the stability of the equilibrium points on the diagram (say stable-dashed, unstable = solid)

Any help is appreciated

Here is my modified codenonlinearsystem2.mw

cheers

A:=plot([seq(Pts(beta)[1][i],i=1..4)],beta=1..4,color=[red,blue,green,maroon]):
B:=plot([seq(Pts(beta)[2][i],i=1..4)],beta=1..4,color=[red,blue,green,maroon]):
plots:-display([A,B]);

@Preben Alsholm  Thanks. This really helped

@Preben Alsholm  Thanks. This really helped

@Markiyan Hirnyk  To make it more clearer, the LHS of eq1, eq2 eq3 represents the RHS of ODE system v1',v2'u2'.

So I want to know the stability of the equilibrium points of the nonlinear system.

Thanks a lot. This really helped.

Thanks a lot. This really helped.