【摘要】：以低頻周期參數(shù)擾動(dòng)下的統(tǒng)一混沌系統(tǒng)為研究對象,應(yīng)用動(dòng)力學(xué)基礎(chǔ)知識,討論了系統(tǒng)的平衡點(diǎn)的分布及其穩(wěn)定性,得到了周期擾動(dòng)系統(tǒng)的靜態(tài)分岔和Hopf分岔的條件。根據(jù)Melnikov方法,計(jì)算得到了系統(tǒng)的同宿軌道以及系統(tǒng)發(fā)生同宿軌道分岔的條件。為了驗(yàn)證理論研究結(jié)果的正確性,采用數(shù)值模擬的方法進(jìn)行了驗(yàn)證,結(jié)果表明理論研究結(jié)果正確。研究結(jié)果可以看做是對周期激勵(lì)的Lorenz類系統(tǒng)和Chen類系統(tǒng)的總結(jié),可以有助于混沌系統(tǒng)在計(jì)算機(jī)應(yīng)用領(lǐng)域的推廣和應(yīng)用。
[Abstract]:Taking the unified chaotic system with low frequency periodic parameter perturbation as the research object, the distribution and stability of the equilibrium point of the system are discussed by applying the basic knowledge of dynamics, and the conditions of static bifurcation and Hopf bifurcation of the system with periodic perturbation are obtained. According to the Melnikov method, the homoclinic orbit of the system and the conditions for the bifurcation of the homoclinic orbit are obtained. In order to verify the correctness of the theoretical results, the numerical simulation method is used to verify the validity of the theoretical results. The results can be seen as a summary of periodic excitation Lorenz class systems and Chen class systems, and can be helpful to the popularization and application of chaotic systems in computer applications.
【作者單位】： 天津大學(xué)機(jī)械工程學(xué)院;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(51479136) 天津市自然科學(xué)基金資助項(xiàng)目(13JCZDJC27100)
【分類號】：O415.5

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