Different silviculture systems were used for harvesting and regeneration of a forest crop. I want to know whether these systems are being practiced in India or other parts of the world.
You may want to start with a review of the 4-volume "Tropical Forestry Handbook" which was updated in 2016. Now in its second edition, it has become the standard reference with many chapters on forest management, mixed tree plantations, natural forest management, species selection, reforestation and it even includes a chapter on agroforestry for climate-smart production. The latter you can find among my publications on ResearchGate.
just as a (historical) side note to your question: A great variety of different systems of silviculture, arboriculture, agroforestry and related practices of forest/wood/tree management have been used throughout human history and in virtually all ecozones and biomes that allowed for such practices. Even in marginal zones that allow(ed) for only limited tree or forest cover, some of these management forms were in practice, often as part of wider systems of landscape management (see, e.g., Aboriginal landcare in Australia). Many of these traditional practices survive to the present day (to varying degrees, of course). In many cases, however, they have been incorporated into or mixed with approaches leaning more heavily towards technology-oriented methods of agroforestry etc.
Thinning is one of the primordial silvicultural practices. It implies always the removal of trees with the main goal of allocating the growing space to those better suited to the wanted productions and yields. to the reduction of competition, anticipation of volume losses due to self-thinning, increase of diameter growth rate, increase of timber value and revenue and reduction of the damages due to the abiotic and biotic disturbances (Matthews, 1989). Mechanical tactics include removal and destruction or rapid removal of infested or infected trees with the objective of destroying the pest. Examples include cutting and burning of trees infested by pests or rapid salvage of infested trees and destruction of infested parts