牛磊，東華大學數學系研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》,《DCDS-A》,《Physica D》, 《Proc. Roy Soc. Edinburgh Sec. A》等。
基本介紹
研究方向,發表論文,
研究方向
微分方程、套用動力系統、生物數學
發表論文
1、(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.
2、(with Mats Gyllenberg and Jifa Jiang) Chaotic attractors in the four-dimensional Leslie–Gower competition model, Physica D: Nonlinear Phenomena, 402 (2020), 132186.
3、(with Mats Gyllenberg and Jifa Jiang) Chaotic attractors in Atkinson–Allen model of four competing species, Journal of Biological Dynamics, 14 (2020), 440–453.
4、(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.
5、(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.
6、(with Mats Gyllenberg and Jifa Jiang) A note on global stability of three-dimensional Ricker models, Journal of Difference Equations and Applications, 25 (2019), 142–150.
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 Qiang Liu) Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM, Mathematical Biosciences and Engineering, 14 (2017), 1247–1259.
13、(with Jifa Jiang and Yi Wang) On heteroclinic cycles of competitive maps via carrying simplices, Journal of Mathematical Biology, 72 (2016), 939–972.
14、(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.
15、(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.
16、(with Jifa Jiang and Daojun Zhu) On the complete classification of nullcline stable competitive three-dimensional Gompertz models, Nonlinear Analysis: R. W. A., 20 (2014), 21–35.
17、(with Jifa Jiang) The dynamical behavior on the carrying simplex of a three-dimensional competitive system: II. Hyperbolic structure saturation, International Journal of Biomathematics, 07 (2014), 1450002.
18、(with Jifa Jiang) The theorem of the carrying simplex for competitive system defined on the n-rectangle and its application to a three-dimensional system, International Journal of Biomathematics, 07 (2014), 1450063.
