Use of the term the “children of Israel” in Judges

[Krupin]

(Ideological, not all Chapter 13, and its beginning)
1 And the children of Israel did evil in the sight of the Lord, and the Lord delivered them into the hands of the Philistines forty years.

[iskander]

Chapter 10:
6 And the children of Israel did evil in the sight of the Lord and served the Baals and the Ashtaroth, and the gods of Syria, the gods of Sidon, the gods of Moab, and the gods of the Ammonites, and the gods of the Philistines; and left the Lord and served Him.
8 They vexed and oppressed the children of Israel eighteen years, all the children of Israel across the Jordan in the land of the Amorites, which is in Gilead.
9 The Ammonites crossed the Jordan to fight also against Judah, Benjamin, and the house of Ephraim. And the children of Israel very closely.
10 And the children of Israel cried to the LORD, and said, We have sinned against thee, because we have forsaken our God and served the Baals.
11 And the LORD said unto the children of Israel: Do not you from the Egyptians, and the Amorites, the Ammonites, and the Philistines,
15 And the children of Israel said to the Lord: We have sinned; do to us whatever you like, but deliver us today.
17 The Ammonites assembled and camped in Gilead; also gathered the children of Israel, and they encamped at Mizpah.

Chapter 11:
4 After some time the Ammonites made war against Israel. (There are no "children of Israel")

Your example 13: 1 is incorrect. Chapter 13 ideological. About her I did not say anything.

It is in 11:33. posted above 11:4
The children of Ammon and the children of Israel have the same significance, they each signify the name of a nation.

http://biblehub.com/interlinear/judges/1-1.htm

[Krupin]

To designate the nation chosen by God used two terms.
1. Israel
2. Children of Israel
Why is the first term used throughout, but the second term (Children of Israel) is distributed non-uniformly?

that's what my question