【正文】 202321402221602 ??????? ??? wbbwbbwE ? Theorem Suppose that (H), hold and Eq.(14) has positive roots. and have the same meaning as last definition. We get ? (1) All root of Eq.(4) have negative real parts for ? and the equilibrium of system (2) is asymptotically stable for . ? (2) If hold , then system (2) undergos a Hopf bifurcation at the equilibrium E, when . I?? *11 ??02 )( 0239。兩個國際合作的研究小組使用了 SEIR數(shù)學模型，對 SARS的傳播趨勢進行分析和預(yù)測，給有關(guān)部門提供了參考意見。 ?由于時滯生物動力系統(tǒng)的演化不僅依賴于系統(tǒng)的當前狀態(tài)，還依賴于系統(tǒng)過去某一時刻或若干時刻的狀態(tài)，其運動方程要用泛函微分方程來描述，和常微分方程系統(tǒng)所描述的系統(tǒng)不同，時滯對系統(tǒng)的動態(tài)性質(zhì)有很大的影響，時滯動力系統(tǒng)一般有無窮多個特征值，解空間是無限維的，其理論分析往往很困難。 if , then the Hopf bifurcation is supercritical (subcritical) and the bifurcation periodic solution exist for 。(8) (9) Set .023423 ???? rqypyy (10) ? Let 4pyz ??, then (10) bees 0113 ??? qzpz(11) where 21 1632 pqp ??, 483221rpqpq ??? Define 3121 )3()2(pq ???231 ????(12) ? Without loss of generality, we assume that Eq.(7) has four positive roots, denoted by , and , respectively. Then Eq.(6) has the four positive roots *kk zv ? )4,3,2,1( ?k we have .)]()[()()()()(sin,)]()[()()())((cos221221213212422122121322124kkkkkkkkkkkkkkkkkkvbbvbbEbbvCvAvbbvDBvvvvbbvbbEbbvCvAvvbbDBvvv??????????????????????(13) ? Denote ? ,)]()[()()())((,)]()[()()()()(22122121322124*2212212132124*kkkkkkkkkkkkkkkkvbbvbbEbbvCvAvvbbDBvvbvbbvbbEbbvCvAvbbvDBvva???????????????????? ?????????????0),2arccos2(10),2(arccos1****ajbvajbvkkjk?????,2,1,0?j kiv?Where k=1,2,3,4。HOPF BIFURCATION IN A SYNAPTICALLY COUPLED FHN NEURON MODEL WITH TWO DELAYS Liping Zhang College of Science, Nanjing University of Aeronautics and Astronautics 2023/07/30 什么是生物數(shù)學？ ? 生物數(shù)學是生物學與數(shù)學之間的邊緣學科，用數(shù)學方法研究和解決生物學問題，也對與生物學有關(guān)的數(shù)學方法進行理論研究。 ? The basic model makes the following assumptions: ? (H) ? ? The model is given by the following system: 021 ?? bbD 0)()( 21 ????? bbCEBA 0)]()()[( 2121 ?????? bbCEBAbbD )1().()()()),(tan h()()()()(),()()()),(tan h()()()()(.423.4.2124333.321.1.21312131.1???????????????????????????txbtxtxtxCtxtaxtxtxtxbtxtxtxCtxtaxtxtx?? ? Fan D, Hong L. Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays. ? Commun Nonlinear Sci Numer Simulat (2023), doi: for FHN neuron model with one delay ? Obviously, E (0,0,0,0) is an equilibrium of system (1), linearizing it gives ? )2().()()()),(()()()()(),()()()),(()()()()(.423.4.2124333.321.1.