【摘要】：在參數(shù)隨機(jī)性影響下,借助Charlier正交多項(xiàng)式逼近,實(shí)現(xiàn)了Duffing映射系統(tǒng)的動力學(xué)行為和隨機(jī)分岔研究。為了明確系統(tǒng)的隨機(jī)特性,首先,對確定性Duffing映射的復(fù)雜動力學(xué)行為進(jìn)行分析,明確其動力學(xué)行為的發(fā)生、發(fā)展和變化規(guī)律;其次,針對系統(tǒng)隨機(jī)參數(shù)的類型,選取相應(yīng)的Charlier正交多項(xiàng)式實(shí)現(xiàn)對隨機(jī)Duffing映射的逼近,得到擴(kuò)階等價(jià)確定性系統(tǒng),進(jìn)而運(yùn)用集合平均響應(yīng)實(shí)現(xiàn)隨機(jī)分岔行為分析。數(shù)值結(jié)果表明,受隨機(jī)因素的影響,倍周期分岔點(diǎn)發(fā)生前移;且系統(tǒng)的收斂區(qū)域隨著隨機(jī)變量強(qiáng)度的增加而縮小。
[Abstract]:Under the influence of parameter randomness, the dynamic behavior and stochastic bifurcation of Duffing mapping system are studied by means of Charlier orthogonal polynomial approximation. In order to clarify the stochastic characteristics of the system, firstly, the complex dynamic behavior of deterministic Duffing mapping is analyzed, and the occurrence, development and variation of the dynamic behavior are clarified. Secondly, the types of random parameters of the system are analyzed. The corresponding Charlier orthogonal polynomials are selected to approximate the stochastic Duffing maps, and the extended equivalent deterministic systems are obtained, and then the stochastic bifurcation behavior analysis is realized by means of the set average response. The numerical results show that the bifurcation point of doubling period moves forward under the influence of random factors, and the convergence region of the system shrinks with the increase of the strength of random variables.
【作者單位】： 西北工業(yè)大學(xué)理學(xué)院;西北工業(yè)大學(xué)力學(xué)與土木建筑學(xué)院;
【基金】：國家自然科學(xué)基金項(xiàng)目(11302171,11672232) 陜西省自然科學(xué)基礎(chǔ)研究計(jì)劃資助項(xiàng)目(2016JQ1015)資助
【分類號】：O174.41

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