, ▁and ▁in ▁chief dom ▁level ▁soci eties ▁world wide ▁has ▁been ▁known ▁for ▁quite ▁a ▁long ▁time , ▁and ▁already ▁in ▁the ▁ 1 9 8 0 s ▁more ▁or ▁less ▁developed ▁mathematical ▁models ▁of ▁dem ographic ▁cycles ▁started ▁to ▁be ▁produced ▁( first ▁of ▁all ▁for ▁Chinese ▁" d yn astic ▁cycles ") ▁( U sh er ▁ 1 9 8 9 ). ▁At ▁the ▁moment ▁we ▁have ▁a ▁considerable ▁number ▁of ▁such ▁models ▁( Ch u ▁and ▁Lee ▁ 1 9 9 4 ; ▁N ef ed ov ▁ 1 9 9 9 , ▁ 2 0 0 2 , ▁ 2 0 0 3 , ▁ 2 0 0 4 ; ▁S . ▁M alk ov , ▁K ov ale v , ▁and ▁A . ▁M alk ov ▁ 2 0 0 0 ; ▁S . ▁M alk ov ▁and ▁A . ▁M alk ov ▁ 2 0 0 0 ; ▁M alk ov ▁and ▁Serge ev ▁ 2 0 0 2 , ▁ 2 0 0 4 a , ▁ 2 0 0 4 b ; ▁M alk ov ▁et ▁al . ▁ 2 0 0 2 ; ▁M alk ov ▁ 2 0 0 2 , ▁ 2 0 0 3 , ▁ 2 0 0 4 ; ▁T urch in ▁ 2 0 0 3 , ▁ 2 0 0 5 a ; ▁Kor ot ay ev ▁et ▁al . ▁ 2 0 0 6 ). ▁ ▁Long ▁cycle ▁theory ▁▁ ▁George ▁Model ski , ▁who