5
x1*x2^2 + x1*x3^2 + x1*x4^2 + x1*x5^2 - 1.1*x1 + 1;
x2*x1^2 + x2*x3^2 + x2*x4^2 + x2*x5^2 - 1.1*x2 + 1;
x3*x1^2 + x3*x2^2 + x3*x4^2 + x3*x5^2 - 1.1*x3 + 1;
x4*x1^2 + x4*x2^2 + x4*x3^2 + x4*x5^2 - 1.1*x4 + 1;
x5*x1^2 + x5*x2^2 + x5*x3^2 + x5*x4^2 - 1.1*x5 + 1;
TITLE : A neural network modeled by an adaptive Lotka-Volterra system, n=5
ROOT COUNTS :
total degree : 243
generalized Bezout bound : 233
with symmetric supporting set structure :
{x1 }{x2 x3 x4 x5}{x2 x3 x4 x5}
{x2 }{x1 x3 x4 x5}{x1 x3 x4 x5}
{x3 }{x1 x2 x4 x5}{x1 x2 x4 x5}
{x4 }{x1 x2 x3 x5}{x1 x2 x3 x5}
{x5 }{x1 x2 x3 x4}{x1 x2 x3 x4}
mixed volume : 233
REFERENCES :
V. W. Noonburg:
"A neural network modeled by an adaptive Lotka-Volterra system",
SIAM J. Appl. Math (1988).
SYMMETRY :
The coefficients have been chosen so that full permutation symmetry
was obtained. The parameter c = 1.1.
------------------------------------------------
| orbit information of list of solutions |
------------------------------------------------
| TYPE | NB <> | NB GEN | NB SOLS |
------------------------------------------------
| 1 2 2 2 2 | 2 | 4 | 20 |
| 1 1 2 2 3 | 3 | 3 | 90 |
| 1 1 1 2 3 | 3 | 3 | 60 |
| 1 1 1 2 2 | 2 | 6 | 60 |
| 1 1 1 1 1 | 1 | 3 | 3 |
------------------------------------------------
| Total number of generating solutions : 19 |
| Total number of generated solutions : 233 |
------------------------------------------------
THE GENERATING SOLUTIONS :
19 5
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -7.73451118106700E-01 -1.41476362957624E-60
x2 : -7.73451118106701E-01 8.07047293847617E-61
x3 : -7.73451118106701E-01 -7.92462101790130E-61
x4 : -7.73451118106701E-01 1.95502345203899E-60
x5 : -7.73451118106703E-01 -4.47279223096270E-61
== err : 2.934E-15 = rco : 1.588E-02 = res : 4.996E-16 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.33372590962199E-01 -4.43586227384486E-01
x2 : -4.33372590962199E-01 -4.43586227384486E-01
x3 : -4.33372590962199E-01 -4.43586227384486E-01
x4 : -9.38352927500085E-01 6.79487362807545E-01
x5 : 1.37172551846228E+00 -2.35901135423059E-01
== err : 3.197E-15 = rco : 2.574E-01 = res : 5.796E-16 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.19537481589068E-01 -5.53617661717944E-01
x2 : -2.19537481589068E-01 -5.53617661717944E-01
x3 : -2.19537481589068E-01 -5.53617661717944E-01
x4 : 1.14746568550757E+00 -4.45985472207374E-01
x5 : 1.14746568550757E+00 -4.45985472207374E-01
== err : 5.944E-16 = rco : 2.034E-01 = res : 2.789E-16 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -6.46857457740524E-01 -7.70636640956298E-02
x2 : -6.46857457740524E-01 -7.70636640956299E-02
x3 : -9.53749557893902E-01 9.98677038789894E-02
x4 : -6.46857457740524E-01 -7.70636640956298E-02
x5 : -9.53749557893902E-01 9.98677038789892E-02
== err : 7.504E-16 = rco : 1.595E-02 = res : 2.797E-16 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -9.53749557893902E-01 -9.98677038789892E-02
x2 : -9.53749557893902E-01 -9.98677038789891E-02
x3 : -6.46857457740523E-01 7.70636640956296E-02
x4 : -6.46857457740524E-01 7.70636640956298E-02
x5 : -6.46857457740524E-01 7.70636640956298E-02
== err : 1.948E-15 = rco : 1.537E-02 = res : 2.317E-16 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -6.51984348487134E-01 -5.84641757363990E-01
x2 : -6.51984348487134E-01 -5.84641757363990E-01
x3 : -6.51984348487134E-01 5.84641757363990E-01
x4 : -6.51984348487134E-01 5.84641757363990E-01
x5 : 1.30396869697427E+00 1.41230388317418E-17
== err : 2.338E-15 = rco : 2.030E-01 = res : 3.608E-16 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.37859037787807E-01 7.28681768047407E-01
x2 : -4.37859037787807E-01 7.28681768047407E-01
x3 : -6.51984348487134E-01 -8.51616563963253E-01
x4 : 1.08984338627494E+00 1.22934795915846E-01
x5 : 1.08984338627494E+00 1.22934795915846E-01
== err : 9.285E-16 = rco : 2.656E-01 = res : 2.483E-16 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.93716127613667E-01 -8.24599937545298E-01
x2 : -1.93716127613667E-01 -8.24599937545298E-01
x3 : 8.66394939329591E-01 -2.82542286504236E-01
x4 : 8.66394939329591E-01 -2.82542286504236E-01
x5 : 8.66394939329591E-01 -2.82542286504236E-01
== err : 8.110E-16 = rco : 2.710E-01 = res : 3.140E-16 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.84962665540328E-02 1.15839619891421E+00
x2 : 5.65907615444606E-01 1.90347351502924E-01
x3 : 5.65907615444606E-01 1.90347351502924E-01
x4 : 5.65907615444606E-01 1.90347351502924E-01
x5 : 5.65907615444606E-01 1.90347351502924E-01
== err : 2.069E-15 = rco : 2.499E-01 = res : 5.579E-16 ==
solution 10 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -9.38352927500085E-01 -6.79487362807545E-01
x2 : -4.33372590962199E-01 4.43586227384486E-01
x3 : -4.33372590962199E-01 4.43586227384486E-01
x4 : -4.33372590962199E-01 4.43586227384486E-01
x5 : 1.37172551846228E+00 2.35901135423059E-01
== err : 3.174E-15 = rco : 1.676E-01 = res : 6.845E-16 ==
solution 11 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -6.51984348487134E-01 8.51616563963253E-01
x2 : -4.37859037787807E-01 -7.28681768047407E-01
x3 : -4.37859037787807E-01 -7.28681768047407E-01
x4 : 1.08984338627494E+00 -1.22934795915846E-01
x5 : 1.08984338627494E+00 -1.22934795915846E-01
== err : 9.384E-16 = rco : 2.440E-01 = res : 4.827E-16 ==
solution 12 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.33372590962199E-01 9.82817291550256E-01
x2 : -4.33372590962199E-01 -9.82817291550256E-01
x3 : 8.66745181924397E-01 -2.56088381459571E-17
x4 : 8.66745181924397E-01 -2.01882508032343E-17
x5 : 8.66745181924397E-01 -2.79407198488834E-17
== err : 4.410E-16 = rco : 2.711E-01 = res : 4.578E-16 ==
solution 13 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -4.84962665540328E-02 -1.15839619891421E+00
x2 : 5.65907615444606E-01 -1.90347351502924E-01
x3 : 5.65907615444606E-01 -1.90347351502924E-01
x4 : 5.65907615444606E-01 -1.90347351502924E-01
x5 : 5.65907615444606E-01 -1.90347351502924E-01
== err : 2.069E-15 = rco : 2.499E-01 = res : 5.579E-16 ==
solution 14 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.86725559053351E-01 4.16737296237545E-01
x2 : 3.86725559053351E-01 4.16737296237545E-01
x3 : 3.86725559053351E-01 4.16737296237546E-01
x4 : 3.86725559053351E-01 4.16737296237546E-01
x5 : 3.86725559053351E-01 4.16737296237545E-01
== err : 6.656E-16 = rco : 2.491E-01 = res : 1.241E-16 ==
solution 15 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.72527361916890E-01 -1.23442380694877E-64
x2 : -3.72527361916890E-01 -1.30594905149215E-65
x3 : -3.72527361916890E-01 1.61424651677917E-64
x4 : -3.72527361916890E-01 1.09199029076238E-64
x5 : 1.83522115087550E+00 -3.56083790465992E-65
== err : 1.546E-15 = rco : 2.298E-01 = res : 1.110E-16 ==
solution 16 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -2.19537481589068E-01 5.53617661717944E-01
x2 : -2.19537481589068E-01 5.53617661717944E-01
x3 : -2.19537481589068E-01 5.53617661717944E-01
x4 : 1.14746568550757E+00 4.45985472207374E-01
x5 : 1.14746568550757E+00 4.45985472207374E-01
== err : 5.944E-16 = rco : 2.034E-01 = res : 2.789E-16 ==
solution 17 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.93716127613667E-01 8.24599937545298E-01
x2 : -1.93716127613667E-01 8.24599937545298E-01
x3 : 8.66394939329591E-01 2.82542286504236E-01
x4 : 8.66394939329591E-01 2.82542286504236E-01
x5 : 8.66394939329591E-01 2.82542286504236E-01
== err : 6.073E-16 = rco : 2.710E-01 = res : 4.003E-16 ==
solution 18 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -8.29137708676524E-01 6.11747293874862E-56
x2 : -7.59287868972322E-01 -1.21074985246066E-56
x3 : -7.59287868972323E-01 -1.35094194064032E-55
x4 : -7.59287868972323E-01 8.53897264366995E-56
x5 : -7.59287868972322E-01 -3.82342058671789E-57
== err : 6.973E-16 = rco : 1.310E-02 = res : 2.220E-16 ==
solution 19 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 3.86725559053351E-01 -4.16737296237545E-01
x2 : 3.86725559053351E-01 -4.16737296237546E-01
x3 : 3.86725559053351E-01 -4.16737296237546E-01
x4 : 3.86725559053351E-01 -4.16737296237545E-01
x5 : 3.86725559053351E-01 -4.16737296237545E-01
== err : 6.692E-16 = rco : 2.491E-01 = res : 2.172E-16 ==