應(yīng)yl7703永利官網(wǎng)楊璐教授邀請，俄羅斯國立高等經(jīng)濟(jì)大學(xué)及俄羅斯下諾夫哥羅德國立大學(xué)Nataliya Stankevich研究員將于2023年9月12日至9月22日訪問我校并作系列學(xué)術(shù)報告。

報告題目一：Generation and destruction of multi-frequency quasi-periodic oscillations

時間：2023年9月19日（星期二）9:30-10:30

地點：理工樓631報告廳

報告題目二：Hyperchaos associated with Shilnikov discrete attractors in different applications

時間：2023年9月19日（星期二）10:30-11:30

地點：理工樓631報告廳

報告摘要：Quasi-periodic oscillations are common in nature and technology. They involve multiple components with different frequencies. Destroying these oscillations creates chaos. Calculating the largest Lyapunov exponents helps identify chaotic dynamics. Oscillations can be categorized as periodic, quasi-periodic, chaotic, or hyperchaotic based on their Lyapunov exponent spectrum. The quasi-periodic Hénon attractor represents another type of chaos with an additional zero exponent. This behavior was first described by Broer H. W., Vitolo R. and Simó Cin. We study simple models and scenarios of torus destruction to understand the emergence of chaos with zero exponents. We provide examples of systems exhibiting these attractors and discuss the universality of multi-frequency quasi-periodic oscillations.

The birth of a hyperchaotic attractor is closely tied to the emergence of an infinite set of cycles. These cycles have a multi-dimensional unstable core and are formed through various local bifurcations in four-dimensional flows. Examples of such bifurcations include torus bifurcation, period-doubling bifurcation, and saddle-node bifurcation. The creation of secondary tori from stable resonance cycles leads to a hierarchy of saddle-foci cycles, resulting in hyperchaos. Additionally, during the absorption of these cycles into the attractor, there is an inverse cascade of bifurcations that gives rise to discrete spiral Shilnikov attractors. This universal scenario, combining hyperchaos and discrete spiral Shilnikov attractors, has been observed in numerous applications, such as radio-physical generators, genetic oscillators, and neuron models. Its prevalence underscores the significance of this phenomenon.

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報告人簡介

Nataliya Stankevich，俄羅斯國立高等經(jīng)濟(jì)大學(xué)及俄羅斯下諾夫哥羅德國立大學(xué)研究員。2007-2011年就讀于俄羅斯薩拉托夫國立大學(xué)獲得博士學(xué)位；2017年在芬蘭Jyv?skyl?大學(xué)獲得數(shù)學(xué)博士學(xué)位。研究方向主要集中在混沌理論及動力系統(tǒng)的復(fù)雜動力學(xué)，包括對混沌吸引子、超混沌行為和非線性動力系統(tǒng)的分析。2019-2022年主持俄羅斯基礎(chǔ)研究基金項目；2021-2023主持芬蘭科學(xué)院雙邊項目；目前主持一項俄羅斯科學(xué)基金項目。

甘肅應(yīng)用數(shù)學(xué)中心

甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級重點實驗室

yl7703永利官網(wǎng)

萃英學(xué)院

2023年9月11日