牛磊研究員
牛磊，1985年11月出生，數學系研究員。主要研究興趣包括連續、離散、隨機動力系統的長時間動力學，特別是系統的整體動力學以及非平凡動力學（如周期軌、擬周期軌、異宿環、混沌等）的存在性及其產生機制。代表性成果發表在《JMPA》,《Nonlinearity》,《SIADS》,《JDE》,《JMB》,《Proc. Roy Soc. Edinburgh Sec. A》,《DCDS-A》,《Physica D》等。2021年入選上海海外高層次人才計劃。
研究方向：
1、 應用動力系統、單調和競爭動力系統、生物數學
近年來承擔的主要科研項目：
1、 2021年主持國家自然科學基金青年科學基金項目
近年來發表的代表性論著：
論文
1、 (with Alfonso Ruiz-Herrera) Simple dynamics in non-monotone Kolmogorov systems, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 153 (2023) , 369–384.
2、 (with Mats Gyllenberg, Jifa Jiang and Ping Yan) Permanence and universal classification of discrete-time competitive systems via the carrying simplex, Discrete and Continuous Dynamical Systems-A, 40 (2020), 1621–1663.
3、 (with Mats Gyllenberg and Jifa Jiang) Chaotic attractors in the four-dimensional Leslie–Gower competition model, Physica D: Nonlinear Phenomena, 402 (2020), 132186.
4、 (with Mats Gyllenberg and Jifa Jiang) Chaotic attractors in Atkinson–Allen model of four competing species, Journal of Biological Dynamics, 14 (2020), 440–453.
5、 (with Lifeng Chen, Zhao Dong, Jifa Jiang and Jianliang Zhai) Decomposition formula and stationary measures for stochastic Lotka–Volterra systems with applications to turbulent convection, Journal de Mathématiques Pures et Appliquées, 125 (2019), 43–93.
6、 (with Janusz Mierczyński and Alfonso Ruiz-Herrera) Linearization and invariant manifolds on the carrying simplex for competitive maps, Journal of Differential Equations, 267 (2019), 7385–7410.
7、 (with Mats Gyllenberg, Jifa Jiang and Ping Yan) On the dynamics of multi-species Ricker models admitting a carrying simplex, Journal of Difference Equations and Applications, 25 (2019), 1489–1530.
8、 (with Alfonso Ruiz-Herrera) Trivial dynamics in discrete-time systems: carrying simplex and translation arcs, Nonlinearity, 31 (2018), 2633–2650.
9、 (with Mats Gyllenberg, Jifa Jiang and Ping Yan) On the classification of generalized competitive Atkinson–Allen models via the dynamics on the boundary of the carrying simplex, Discrete and Continuous Dynamical Systems-A, 38 (2018), 615–650.
10、(with Jifa Jiang) On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex, Journal of Mathematical Biology, 74 (2017), 1223–1261.
11、(with Jifa Jiang) On the validity of Zeeman’s classification for three dimensional competitive differential equations with linearly determined nullclines, Journal of Differential Equations, 263 (2017), 7753–7781.
12、(with Jifa Jiang and Yi Wang) On heteroclinic cycles of competitive maps via carrying simplices, Journal of Mathematical Biology, 72 (2016), 939–972.
13、(with Jifa Jiang) On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points, Discrete and Continuous Dynamical Systems-A, 36 (2016), 217–244.
14、(with Xiaojing Chen and Jifa Jiang) On Lotka–Volterra equations with identical minimal intrinsic growth rate, SIAM Journal on Applied Dynamical Systems, 14 (2015), 1558–1599.
主要學術兼職：
1、美國數學學會《數學評論》評論員
2、歐洲數學學會會員
Mathematicians I have had the honor to collaborate with
Zhao Dong (Chinese Academy of Sciences)
Mats Gyllenberg (University of Helsinki)
Jifa Jiang (Shanghai Normal University)
Janusz Mierczyński (Wroc?aw University of Science and Technology)
Alfonso Ruiz-Herrera (Universidad de Oviedo)
Yi Wang (University of Science and Technology of China)
