I want to study the composition techniques used in following drawings found from a Google search.
What should I look for in Google to read about this drawing pattern/technique?
I would classify these images as line art.
With line art you will see clear lines defining forms and shapes, and sometimes where color and light would be, but the color and shading won't be there.
Definition is enhanced in compositions such as the ones posted by varying the line weight and and stroke. The thicker lines make parts stand out, and also help define depth.
Since the line weights vary in these examples, they may have been drawn using some type of ink (presuming they weren't digitally produced). Pen and marker tips allow for more variation in line weight than a typical pencil, although it's possible to sharpen a pencil in such away to allow for more variation.
Line art itself isn't going to be subject to less rules of composition than other 2D visual arts. An understanding of composition in general is going to be helpful, although outside the scope of this answer.
However, certain techniques or media may be more helpful to practice with, if the end goal is this type of art: Drawing in general, inking or other practice to help with line weights, and making clean lines.
Making clean lines can be achieved by learning how to use such tools as French curves, templates, stencils and compasses:
Here's an example of some French curves:
A basic foundation in compositional concepts will apply to all types of art, from scrape-booking to sculpture and architecture. It would seem to be especially valuable when a drawing has so many elements as these do. Without compositional aides, a drawing could become a confusing visual blur or a flat pattern.
Decide what elements you want to focus on - the main idea. There can also be secondary foci, so that your eye moves across a drawing. In the lower drawing, with the birds and butterflies, romanticized flight/wings seem to be the theme here. The top butterfly and bird seem to be focal points along with the bottom butterfly. The groupings balance each other, giving weight and focus to both the top and bottom of the drawing, in spite of the fancifully airy nature of the drawing.
Techniques that add dimensional depth are clearly seen here. Perspective makes it appear as though the elements are spiraling downwards away from us and disappearing towards the center of the page. Perspective is summoned in several ways: overlapping, line weight, and the paleness of the more "distant" objects. When objects overlap, even in a drawing, our brains interpret the partially blocked objects as being behind the others and therefore, farther away. For example, on the outer edge of the drawing, rhododendron-like flowers overlap the vines. This makes the flowers pop towards us while in the center, one bird overlaps another.
The line weights vary across the drawing. Darker lines do two things here - they denote object boundaries in space and denote atmospheric perspective. Where a line marks the boundary between an object and open space, it's darker, like in the body outline of the upper right bird. Lines on the bird's body that relate detail, but are not free-standing in space, were given a lighter weight, as in the feathers. When you observe a panoramic landscape, you see that the lines (and colors) that are closer to you have more weight and vibrancy, while as space recedes, the lines and colors become less vibrant, more pale, and more greyed-out. This is called atmospheric perspective. Compare the heavy lies of those rhododendron-like flowers that pop out towards us with the soft, thin lines of the terminal tip of the vine at the center of the drawing. That tip fades into the distance, contributing to an impression of depth in the drawing.
Proportion also aides the impression of depth. Unfortunately, it's less obvious here. Two similar objects (species of bird, flower, or butterfly) should be about the same size unless one is "farther away" to it's twin. The only object that really does that here is the spiraling vine. Along the outer edge of the drawing, the vines are drawn with more line weight showing the boundary between solid and space, that they are closer to us than the terminal tip in the center is, and the diameter of those vines are proportionally thicker at the outer edge than those tender terminals that seem farther away.
This link provides a brief discussion of common compositional concepts: "Drawing for Dummies"