Willis环状脑动脉瘤生物数学模型的渐近解

!∀!!,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,!∀#∀,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,r,eos(,,,a=0(1),,+,=,;,,;),,)exp(21,;,,,,,,,,i,,,,*,,,,(11)1,,)exP(z,,,),,,(rl),,,+,,,,,,,)=,,,,,lwe,,,,,,,,1)+,,,1)+eosR-,,R,,,,,,,,,,3,,,,E,,,,,,T,,,,x)+,,,z)+,,+,+,=,x,)exp(f,,+,,,,+,:,),:,A,:,A,)exp(21,,)exp(31,A,,,exp,,,exp,;)exp,,)exp,:)exp,,)exp,;),:),,,:)+,,;)+s,;),:)=o1,;,=,:,exp(,,,),,=,3,(22),,,,,,21,+,;)exP(i,:,,,1),1)3Yz,_,,,.,k,,z)exp(1.,R,,=R,,,8,,,g,,,,+,)=0.,:,,,),,,,,,,,,,,,/,,+!,,,:,,,,,,,,,,A,,,,,,,,,,,,,,,,,,,,,l:T,1972,21:165~1732,,19,1971,225~238Nayfe,MookDT,305~32584,~.,r.,,K,YunnanUniversity)AbstractInthispaper,westudythebiomathematiealmodelofaneurxsmofeireleofwillis.Weobatinapproximationsolutionsofthesystemundertheeonditionofweakdampingandthefrequeney,therelat,exter,resonanee,frequeneyrespons,(,,,hastwohonzoelinieorbits,,,andafanuilvofperiodieorbitsI,wehaveobtainedeonditionw,hasasubhamonicorbitUnderaeonditionweliaveprovodthatsomeiterate(P,hasaSmaleliorseshoe,i.e.thesolutionsof(2),areeliaotie.Thistheoretieresultindieatesthatwithintheflow,t,,biomathematiealmodel,bifureation,ehaos.