| Summary: | St e llar mode ls of b e t wee n 4~ N 0 ~nd 600M o are co nst ruct ed with electron s catt er ing opacity)and a lso with mo r e moder n op a citi es . Lin e a r ad i a bat ic stability an a lysis is th e n applied to th e se ffi odels) and th e pe riods and di ssip a tion p~op e rties of th e fir st six puls a tional modes obtained. It is found th a t the first few h a r monic s do not ddcay r ap idly co mpared to th ~ fundamental p e riod and also that one has a series of resonances J starting with u first harmonic reson a nc e at a bou t th e critical mass. Th e re sonan c e th en shi f ts to hi ghe r mod e s as the mass is incr e ase d. Si mp l e r non line a r sy s t ems a~e discuSsed with a view to shewing ho ~ th ese re s on an c es can be i mp ort ant. A stability tr ea t me nt of the p~ricJic a l1y 0scill at ing homoge nou s star is givenland'ls;ymptotic theory discus sed . It is found th a t in these syst em~ reso na nce play s a vital role. I\, non lin ;: ar techn iq ue ba SEd on finit e differ Ance techni q ues is th e n a p p li e d to ~ his problem. The method we use is that of a W factor as us ed by oth e r , authors) but it is re19.xed to unity. Tt is found that this is a mor~ co mp licated problem th a n m~ y at first be thought ~ Severely modulated - quasi periodic s~lUtions c a n be obt a ined I as well as so l utions sh o~ in g b e9 t ~ype pheno me na. Horeover)th~se effects ffiay c a use li mit a tion at a lower amplitude th a n has b een o bta in ed ~he r e l a ti o nship b etwee n the dir e c~ integ ra tions and asymptotic th e o r y is dis cussed . Fin a lly/ as far a s is possible) t hi s .,ork is COnl l ,al'c d ·with t hat of oth e r authors.
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