We exhibit calculating formula about direction of hopf bifurcation and the bifurcation periodic solutions in the first bifurcated to and so on with norm form theory and center mainfold theorem , furthermore , we carry out numerical simulated compution with mathematica . finally , the charting are performed with mat - lab 我们还用中心流形和规范形理论，给出了在第一个分支点_ 0处的hopf分支方向，分支周期解的稳定性的计算公式。
4 . engineering dhqase ( arod ) - deficient e . coli mutant with a second copy of the arob gene gene targeting technique was used to disrupt the arod gene in e . coli chromosome . the mutant 31bk was engineered , in which homologous recombination of the arobkanr gene cassette into the arod locus ( arod : : arobkanr ) of the e . coli strain atcc31884 genome utilized the helper plasmid pkd46 with red system . the host cell 31bk lacked catalytic activity of dhqase ( arod ) and had a second copy of the arob gene , so it improved carbon flow into the quinic acid biosynthesis direction 构建宿主菌基因精确定位突变株31bk ( arod : : arobkan ~ r )为了改变代谢途径脱氢奎尼酸( dhq )分支点上的代谢流量，使之充分流向目的产物奎尼酸合成方向，利用基因打靶技术构建了31884宿主菌arod基因精确定位插入突变体，使dhq脱水酶( dhqase )失活，阻断了碳代谢流流向芳香氨基酸生成的方向，同时用同源重组的方法将arob基因定位整合入染色体上，解除了限速酶对碳代谢流通过共同途径到达dhq的阻遏影响，并减轻代谢负担。
On the assumption that workstation was known , we started from working procedure table , educed pretreatment working procedure table based on original time and then obtained c orrelating information such as priority area , embranchment , embranchment point . we obtained optimum scheduling of garment suspending line using ga 即在工作地数目已知的前提下，从工序分析表出发，根据初始节拍得出预处理过的工序分析表，然后从中获取相关信息：优先权区域、分支信息、分支点等信息，运用遗传算法求得服装吊挂生产线的优化调度。
For instance , embranchment working procedure , embranchment point working procedure , working procedure total , working procedure and correspond process time . moreover , this thesis worked out priority area chart . it was based on successively sequence of process manufacture and principle to lessen number of one man working more machine to the best of our abilities 从预处理过的工序分析表可以找出分支工序、分支点工序、工序总数、各工序及相应工序的加工时间等数据信息，另外根据工序加工的先后顺序和尽量减少一人多机的原则，做出了优先权区域图。
In the second section , by means of local bifurcation theories [ 17 ] , we have proved the system generate bifurcation at the semi - trivial solutions ( uo , 0 ) , ( 0 , v0 ) . furthermore , using stability theory [ 16 ] [ 17 ] , we analyze the stability of the positive solutions near the bifurcating points and get ideal results 川、 n吻）处出现正解分支，运用稳定性理论分析‘卜nn并得到了分支点附近的正解的稳定性情况，成功的解决了反应扩散方程研究中的一个基本问题：平衡解的稳定性
