If we were to work through the mathematics, we would need to solve (3.68) and (3.70) to get a relationship between x 1, x 2, x 3, and x 4 for each equation. The equations to get the x 2-nullcline and x 4-nullcline are quite complicated. Similarly, the x 3-nullcline is defined by points in four-dimensional space such that x 4 = 0. The x 1-nullcline is defined by points in four-dimensional space such that x 2 = 0. The expressions for the x 1-nullcline and x 3-nullcline are relatively simple. Furthermore, we aren’t able to visualize these nullclines because they are subsets of four-dimensional space. Unfortunately, because this is a fourth-order system, the mathematics becomes much more difficult to work through.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |