Sentence examples for trivial branch from inspiring English sources

In Section 2, we show global bifurcation phenomena from the trivial branch with the leftward direction.

In Section 2, we show a global bifurcation phenomena from the trivial branch with rightward direction.

After identifying a trivial branch, we combine computation and analysis to determine the stability and bifurcations of solutions along this branch.

In this section, we state some preliminary results and show global bifurcation phenomena from the trivial branch with the leftward direction.

This implies we have a branch of positive solutions bifurcating from the trivial branch of solutions ( a, 0 ) at ( 0, 0,).

In this section, we state some preliminary results and show a global bifurcation phenomenon from the trivial branch with rightward direction.

First, all of the trivial branches are added to the tree.

This process is repeated for each non-trivial branch.

Every non-trivial branch has two taxa on one side and three on the other.

Initially, every element of the vector is set to 0. A non-trivial branch is selected and the associated partition is created by putting all taxa on one side of the branch into the first group in the partition and all other taxa in the second.

Super- and sub-critical Hopf bifurcations in the trivial as well as non-trivial branches and the saddle-node or fold type bifurcations in the non-trivial branches of the response curves are found.