应304am永利集团官网杨璐教授邀请，俄罗斯国立高等经济大学及俄罗斯下诺夫哥罗德国立大学Nataliya Stankevich研究员将于2023年9月12日至9月22日访问我校并作系列学术报告。

报告题目一：Generation and destruction of multi-frequency quasi-periodic oscillations

时间：2023年9月19日（星期二）9:30-10:30

地点：理工楼631报告厅

报告题目二：Hyperchaos associated with Shilnikov discrete attractors in different applications

时间：2023年9月19日（星期二）10:30-11:30

地点：理工楼631报告厅

报告摘要：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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报告人简介

Nataliya Stankevich，俄罗斯国立高等经济大学及俄罗斯下诺夫哥罗德国立大学研究员。2007-2011年就读于俄罗斯萨拉托夫国立大学获得博士学位；2017年在芬兰Jyväskylä大学获得数学博士学位。研究方向主要集中在混沌理论及动力系统的复杂动力学，包括对混沌吸引子、超混沌行为和非线性动力系统的分析。2019-2022年主持俄罗斯基础研究基金项目；2021-2023主持芬兰科学院双边项目；目前主持一项俄罗斯科学基金项目。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

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萃英学院

2023年9月11日