CAJ | 학술논문

运用正交多项式逼近原理，研究了分数阶随机 Duffing 系统在零平衡点的 Hopf 分岔。首先，运用Laguerre 正交多项式逼近法将含有随机参数的分数阶 Duffing 系统转化为等价的确定性系统，然后通过数值计算求得其响应。最后，利用两个引理求得等价系统发生 Hopf 分岔行为的临界值，并通过数值模拟验证了理论分析结果。
운용정교다항식핍근원리，연구료분수계수궤 Duffing 계통재령평형점적 Hopf 분차。수선，운용Laguerre 정교다항식핍근법장함유수궤삼수적분수계 Duffing 계통전화위등개적학정성계통，연후통과수치계산구득기향응。최후，이용량개인리구득등개계통발생 Hopf 분차행위적림계치，병통과수치모의험증료이론분석결과。
According to the theory of orthogonal polynomial,the Hopf bifurcation of fractional-order stochastic Duffing system at zero balance point is studied.Firstly,converting the fractional-order stochastic Duffing system into its equivalent deterministic one by using Laguerre orthogonal polynomial approximation principle.its response is obtained in the numerical calculation.Finally,it can using two lemmas to get the critical value of Hopf bifur-cation in equivalent system,and the theoretical analysis results are verified by numerical simulation.