Diversity in Competitive Threshold Linear Networks

Figure 1 — Directed Network Which Represents Threshold Linear Network

Adjacency Matrix Representing Directed Network

$$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$$

Figure 2 — Solution Via Numerically Solving Differential Equation

Initial Conditions

The initial conditions applied to the network above are the following:

• $x1[0] = .9$
• $x2[0] = x3[0] = x4[0] = x5[0] = x6[0] = x7[0] = x8[0] = x9[0] = x10[0] = .5$

Figure 3 — Dynamics of Directed Network Which Represents Competitive Threshold Linear Network