本文選題：兩時(shí)間尺度　切入點(diǎn)：點(diǎn)-點(diǎn)式簇發(fā)　出處：《河南科技大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年04期 　論文類型：期刊論文

【摘要】：以非自治杜芬-范德波爾振子為例,探討了當(dāng)外激勵(lì)頻率與系統(tǒng)固有頻率之間存在量級差異,也即存在頻域不同尺度時(shí)的快慢耦合效應(yīng)。通過固定低頻激勵(lì)項(xiàng),分析了快子系統(tǒng)的穩(wěn)定性和分岔行為,得到了對應(yīng)的兩參數(shù)分岔集。將分岔集劃分為5個(gè)區(qū)域,并分析了與各區(qū)域相關(guān)的簇發(fā)振蕩模式。揭示了對稱式折/折和對稱式亞臨界Hopf/亞臨界Hopf等點(diǎn)-點(diǎn)式簇發(fā)的行為,以及對稱式亞臨界Hopf/極限環(huán)折和對稱式延遲超臨界Hopf/延遲超臨界Hopf等點(diǎn)-圈式簇發(fā)的行為。研究結(jié)果表明:快子系統(tǒng)的多解和多分岔共存是誘發(fā)各種對稱式簇發(fā)振蕩模式的重要原因。
[Abstract]:Taking the nonautonomous Duffin-van der Bohr oscillator as an example, the order of magnitude difference between the external excitation frequency and the natural frequency of the system is discussed, that is, the fast-slow coupling effect with different scales in the frequency domain. The stability and bifurcation behavior of the fast subsystem are analyzed, and the corresponding two parameter bifurcation sets are obtained. The bifurcation set is divided into five regions. The cluster oscillation modes related to each region are analyzed, and the behavior of symmetric folded / folded and symmetric subcritical Hopf/ subcritical Hopf is revealed. The behavior of symmetrically subcritical Hopf/ limit cycles and symmetric delayed-supercritical Hopf/ delayed-supercritical Hopf cluster is also studied. The results show that the coexistence of multiple solutions and multiple bifurcations of fast subsystems induces all kinds of symmetric clusters. An important reason for oscillating mode.
【作者單位】： 江蘇大學(xué)土木工程與力學(xué)學(xué)院;
【基金】：國家自然科學(xué)基金項(xiàng)目(11632008,11572141,11502091,11472115,11402226)
【分類號】：O32
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本文編號：1631470