Hello Ijasz,
The composite bow underwent quite some transformation from the Scythian form circa 500 bce to the Magyars of the 10thC or the Mongols of the 13thC. In fact, its history goes back further still, to ancient Egypt. The introduction of rigid siyahs to the limb tips went some way to increasing the draw length but they are in no way necessary for this, as can be seen in Korean bows. These little bows draw 32"+ and their limbs achieve frightening angles. The siyahs of these bows are constructed in a different way and do flex. Though the dimensions of these two bows are similar, the Scythian did not possess the flat limbs and are almost as thick as they are wide.
Steppe tactics were pretty similar throughout the various peoples: Scythians, Sarmatians, Huns, Avars, Magyars, Khazars, Pechenegs, Qipchaqs. Usually the enemy was denied engagement and harried until drawn out of formation by feigned retreat or overimpetuousness. At this point various bands, often operating as family groups would gallop into the confusion, loosing their arrows as they went. In fact, it can be likened to their herding techniques in some respects, the Huns in particular used lassos to devastating effect.
The larger bows of the Huns evolved into a shorter, more reflexed weapon and supposedly reached its zenith with the Turkish design.
You are in Hungary, have you been to the National Museum in Budapest? It's a place I've been wanting to go for ages. Plenty of artefacts relating to these steppe nomads.
There are many books that cover the subject but more in a historical study of each timeframe rather than a study of the composite bow. If you want to find out about the Magyars or the Avars and such without reading indepth books, the Osprey series are quite good. They contain a fair amount of historical information, brief descriptions of any memorable battles and colour plates depicting arms and armour, based on archaeological finds.