#!/usr/bin/octave

% Octave file: a figure for the file instability.tex

gset output "instability-fig-counterexample.tex"
gset term pstex norotate

%gset output "instability-fig-counterexample.ps"
%gset term postscript color

% Clear labels and arrows:
%gset nolabel
%gset noarrow

gset nokey
gset zeroaxis
gset nogrid
gset noborder
gset ticscale 1
gset noxtics
gset noytics
gset size 0.95,0.6
%gset linestyle 1 linewidth 3
xi=(-2:0.05:2)';
Xaxis=[0.0+xi,xi.*.0];
xi=(0.:0.05:2)';
Yaxis=[0.0+xi.*0,xi.+0.0];

gset label '{\\it stable stationary states}' at -1.6,0.1
gset label '{\\it unstable stationary states}' at 0.4,0.1

%gset label '$\\omega=0$' at -0.1,-0.1
gset label '$0$' at 0.05,-0.1
%gset label '$\\omega$' at 1.8,-0.1

%arrow([1,1],1,0,1);


xi=(0:0.1:6.3)';
circ1=[0.3.*cos(xi),0.3.*sin(xi)];
circ2=[0.6.*cos(xi),0.6.*sin(xi)];
xi=(-1.7:0.1:3.6)';
circ3=[0.9.*cos(xi),0.9.*sin(xi)];
xi=(-1.7:0.1:4.2)';
circ4=[1.2.*cos(xi),1.2*sin(xi)];
xi=(0:0.1:6.3)';
circ5=[1.5.*cos(xi),1.5*sin(xi)];
circ6=[1.8.*cos(xi),1.8*sin(xi)];

a=-0.25;
b=-1.18;


gplot [-2:2] [-1.5:1.5] \
    circ1 using 1:2  with dots, \
    circ2 using 1:2  with dots, \
    circ3 using 1:2  with dots, \
    circ4 using 1:2  with dots, \
    [a-.04,b+0.0] with dots,\
    [a+.002, b+.225] with dots,\
    [a-.19,b+.09] with dots,\
    [a-.18,b+.3] with dots,\
    [a-.25,b+.46] with dots,\
    [a-.33,b+.62] with dots,\
    [a-.44, b+.63] with dots,\
    [0,1.2,-0.16,0] with vector 1,\
    [0,0.9,-0.12,0] with vector 1,\
    [0,0.6,-0.08,0] with vector 1,\
    [0,0.3,-0.04,0] with vector 1,\
    [0,-1.2,-0.16,0] with vector 1,\
    [0,-0.9,-0.12,0] with vector 1,\
    [0,-0.6,-0.08,0] with vector 1,\
    [0,-0.3,-0.04,0] with vector 1,\
    [1.2*sqrt(3)*0.5,1.2*0.5,-0.12,0.12*sqrt(3)] with vector 1,\
    [0.9*sqrt(3)*0.5,0.9*0.5,-0.09,0.09*sqrt(3)] with vector 1,\
    [0.6*sqrt(3)*0.5,0.6*0.5,-0.06,0.06*sqrt(3)] with vector 1,\
    [0.3*sqrt(3)*0.5,0.3*0.5,-0.03,0.03*sqrt(3)] with vector 1,\
    [-1.2*sqrt(3)*0.5,1.2*0.5,-0.12,-0.12*sqrt(3)] with vector 1,\
    [-0.9*sqrt(3)*0.5,0.9*0.5,-0.09,-0.09*sqrt(3)] with vector 1,\
    [-0.6*sqrt(3)*0.5,0.6*0.5,-0.06,-0.06*sqrt(3)] with vector 1,\
    [-0.3*sqrt(3)*0.5,0.3*0.5,-0.03,-0.03*sqrt(3)] with vector 1,\
    [1.2*sqrt(3)*0.5,-1.2*0.5,-0.12,-0.12*sqrt(3)] with vector 1,\
    [0.9*sqrt(3)*0.5,-0.9*0.5,-0.09,-0.09*sqrt(3)] with vector 1,\
    [0.6*sqrt(3)*0.5,-0.6*0.5,-0.06,-0.06*sqrt(3)] with vector 1,\
    [0.3*sqrt(3)*0.5,-0.3*0.5,-0.03,-0.03*sqrt(3)] with vector 1,\
    [-1.2*sqrt(3)*0.5,-1.2*0.5,-0.12,0.12*sqrt(3)] with vector 1,\
    [-0.9*sqrt(3)*0.5,-0.9*0.5,-0.09,0.09*sqrt(3)] with vector 1,\
    [-0.6*sqrt(3)*0.5,-0.6*0.5,-0.06,0.06*sqrt(3)] with vector 1,\
    [-0.3*sqrt(3)*0.5,-0.3*0.5,-0.03,0.03*sqrt(3)] with vector 1,\
    [0,0] with points, \
    Xaxis with lines;