【摘要】：在參數(shù)隨機性影響下,借助Charlier正交多項式逼近,實現(xiàn)了Duffing映射系統(tǒng)的動力學行為和隨機分岔研究。為了明確系統(tǒng)的隨機特性,首先,對確定性Duffing映射的復雜動力學行為進行分析,明確其動力學行為的發(fā)生、發(fā)展和變化規(guī)律;其次,針對系統(tǒng)隨機參數(shù)的類型,選取相應的Charlier正交多項式實現(xiàn)對隨機Duffing映射的逼近,得到擴階等價確定性系統(tǒng),進而運用集合平均響應實現(xiàn)隨機分岔行為分析。數(shù)值結果表明,受隨機因素的影響,倍周期分岔點發(fā)生前移;且系統(tǒng)的收斂區(qū)域隨著隨機變量強度的增加而縮小。
[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)大學理學院;西北工業(yè)大學力學與土木建筑學院;
【基金】：國家自然科學基金項目(11302171,11672232) 陜西省自然科學基礎研究計劃資助項目(2016JQ1015)資助
【分類號】：O174.41

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本文編號：2292807