noon5 -- A neural network modeled by an adaptive Lotka-Volterra system with 5 variables

Synopsis

Usage:

noon5(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of the polynomials in the system

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 233 solutions found in 0.582 seconds (with a Bezout bound of 243).

The coefficients have been chosen so that full permutation symmetry was obtained.

Reference: "A neural network modeled by an adaptive Lotka-Volterra system" by V.W. Noonburg.

See also: http://homepages.math.uic.edu/~jan/Demo/noon5.html.

i1 : noon5(RR_53)

         2      2      2      2               2        2      2      2  
o1 = {x x  + x x  + x x  + x x  - 1.1x  + 1, x x  + x x  + x x  + x x  -
       1 2    1 3    1 4    1 5       1       1 2    2 3    2 4    2 5  
     ------------------------------------------------------------------------
                 2      2        2      2               2      2      2    
     1.1x  + 1, x x  + x x  + x x  + x x  - 1.1x  + 1, x x  + x x  + x x  +
         2       1 3    2 3    3 4    3 5       3       1 4    2 4    3 4  
     ------------------------------------------------------------------------
        2               2      2      2      2
     x x  - 1.1x  + 1, x x  + x x  + x x  + x x  - 1.1x  + 1}
      4 5       4       1 5    2 5    3 5    4 5       5

o1 : List

Ways to use noon5 :

noon5(Ring)

For the programmer

The object noon5 is a method function.