ently ▁the ▁most ▁important ▁contributions ▁to ▁the ▁development ▁of ▁the ▁mathematical ▁models ▁of ▁long - term ▁(" sec ular ") ▁soci ode m ographic ▁cycles ▁have ▁been ▁made ▁by ▁Serge y ▁N ef ed ov , ▁Peter ▁T urch in , ▁And rey ▁Kor ot ay ev , ▁and ▁Serge y ▁M alk ov . ▁What ▁is ▁important ▁is ▁that ▁on ▁the ▁basis ▁of ▁their ▁models ▁N ef ed ov , ▁T urch in ▁and ▁M alk ov ▁have ▁managed ▁to ▁demonstrate ▁that ▁soci ode m ographic ▁cycles ▁were ▁a ▁basic ▁feature ▁of ▁complex ▁agr arian ▁systems ▁( and ▁not ▁a ▁specifically ▁Chinese ▁or ▁European ▁phenomen on ). ▁ ▁The ▁basic ▁logic ▁of ▁these ▁models ▁is ▁as ▁follows : ▁ ▁After ▁the ▁population ▁reaches ▁the ▁ce iling ▁of ▁the ▁carrying ▁capacity ▁of ▁land , ▁its ▁growth ▁rate ▁decl ines ▁toward ▁near - zero ▁values . ▁ ▁The ▁system ▁experiences ▁significant ▁stress ▁with ▁decl ine ▁in ▁the ▁living ▁standards ▁of ▁the ▁common ▁population , ▁increasing ▁the ▁sever ity ▁of ▁fam ines , ▁growing ▁re bell ions ▁etc . ▁ ▁As ▁has ▁been ▁shown ▁by ▁N ef ed ov , ▁most ▁complex ▁agr arian ▁systems ▁had ▁considerable ▁res erves ▁for ▁stability , ▁however , ▁within ▁ 5 0 – 1 5 0 ▁years ▁these ▁res erves ▁were ▁usually ▁exha usted ▁and ▁the ▁system ▁experienced ▁a ▁dem ographic ▁collapse ▁( a ▁Mal th us ian ▁cat ast rop he ), ▁when ▁increasing ly ▁severe ▁fam ines , ▁ep ide m ics , ▁increasing ▁internal ▁war fare