# 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.

 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