Zhongwei Shen

University of Alberta
Department of Mathematical and Statistical Sciences
University Commons 5-140
Edmonton, AB T6G 2N8

Office: University Commons 4-263
Email: zhongwei@ualberta.ca
I am an Associate Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta.
Here is my Curriculum Vitae.

Research Interests

My research spans Dynamical System, PDE, and Stochastic Analysis. Topics of current interest include:

  • Stochastic dynamics: stationary and quasi-stationary distributions, stochastic stability/bifurcation, Large deviation principle, transient dynamics and metastability, transient chaos, and applications in fluid dynamics, non-equilibrium statistical physics, population dynamics, etc.
  • Data-driven dynamical systems: Koopman theory and spectrum learning
  • Front/Wave propagation and global dynamics: transition fronts, forced traveling waves and climate change, principal spectral theory, and applications in ecology, epidemiology, etc.

    • Stochastic dynamics

    1. Quasi-potential of stationary and quasi-stationary densities: existence, regularity, and applications.
      Submitted. (with Chenchen Mou, Weiwei Qi, and Yingfei Yi)
    2. Stochastic stability of physical measures in conservative systems.
      Submitted. (with Weiwei Qi and Yingfei Yi)
    3. Quasi-stationary distributions of absorbed singular diffusion processes in higher dimensions.
      Submitted. (with Alex Hening, Weiwei Qi, and Yingfei Yi)
    4. Mesoscopic and macroscopic entropy balance equations in a stochastic dynamics and its deterministic limit.
      J. Stat. Phys., 192 (2025), no. 8, Paper No. 107. (with Hong Qian)
    5. Population dynamics under demographic and environmental stochasticity.
      Ann. Appl. Probab., 34 (2024), no. 6, 5615-5663. (with Alex Hening, Weiwei Qi, and Yingfei Yi)
    6. Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions.
      Probab. Theory Related Fields, 188 (2024), no. 1-2, 667-728. (with Weiwei Qi and Yingfei Yi)
    7. Concentration of quasi-stationary distributions for one-dimensional diffusions with applications.
      Ann. Inst. Henri Poincaré Probab. Stat., 60 (2), 874-903. (with Shirou Wang and Yingfei Yi)
    8. Transient dynamics of absorbed singular diffusions.
      J. Dynam. Differential Equations, 34, 3089 - 3129 (2022). (with Min Ji, Weiwei Qi, and Yingfei Yi)
      Special issue in memory of Professor Genevieve Raugel.
    9. Convergence to periodic probability solutions in Fokker-Planck equations. Supplementary Materials
      SIAM J. Math. Anal. 53 (2021), no. 2, 1958-1992. (with Min Ji, Weiwei Qi, and Yingfei Yi)
    10. Towards mesoscopic ergodic theory.
      Science China Mathematics 63 (2020) no. 9, 1853-1876. (with Weiwei Qi, Shirou Wang, and Yingfei Yi)
      Special issue in memory of Professor Shantao Liao.
    11. Noise-vanishing concentration and limit behaviors of periodic probability solutions.
      Differential Integral Equations 33 (2020), no. 5-6, 273-322. (with Min Ji, Weiwei Qi, and Yingfei Yi)
    12. Existence of periodic probability solutions to Fokker-Planck equations with applications.
      J. Funct. Anal. 277 (2019) 108281. (with Min Ji, Weiwei Qi, and Yingfei Yi)
    13. Quantitative concentration of stationary measures.
      Physica D: Nonlinear Phenomena 399 (2019) 73-85. (with Min Ji and Yingfei Yi)
    14. Convergence to equilibrium in Fokker-Planck equations.
      J. Dynam. Differential Equations 31 (2019), 1591-1615. (with Min Ji and Yingfei Yi)
      Special issue in memory of Professor George R. Sell.
    15. Asymptotic dynamics of a class of coupled oscillators driven by white noises.
      Stoch. Dyn., 13 (2013), no. 4, 1350002. (with Wenxian Shen and Shengfan Zhou)
    16. Synchronization of coupled stochastic systems with multiplicative noise.
      Stoch. Dyn., 10 (2010), no.3, 407-428. (with Shengfan Zhou and Xiaoying Han)
    17. One-dimensional random attractor and rotation number of the stochastic damped sine-Gordon equation.
      J. Differential Equations, 248 (2010), no.6, 1432-1457. (with Shengfan Zhou and Wenxian Shen)

    Data-driven dynamical systems

    1. A data-driven framework for Koopman semigroup estimation in stochastic dynamical systems.
      Chaos, to appear. (with Yuanchao Xu, Kaidi Shao, Isao Ishikawa, Yuka Hashimoto, and Nikos Logothetis)
    2. ResKoopNet: learning Koopman representations for complex dynamics with spectral residuals.
      ICML 2025. (with Yuanchao Xu, Kaidi Shao, and Nikos Logothetis)

    Front/Wave propagation and global dynamics

    1. Shape optimization of principal eigenvalues and the geometry of climate envelopes.
      Submitted. (with Xiao Zhao)
    2. From habitat decline to collapse: a spatially explicit approach connecting habitat degradation to destruction.
      Submitted. (with Yurij Salmaniw and Hao Wang)
    3. Population dynamics under climate change: persistence criterion and effects of fluctuations.
      J. Math. Biol., 84, 30 (2022). (with Wenxian Shen, Shuwen Xue, and Dun Zhou)
    4. Global dynamics of a diffusive competition model with habitat degradation.
      J. Math. Biol., 84, 18 (2022). (with Yurij Salmaniw and Hao Wang)
    5. Nonlocal dispersal equations in time-periodic media: principal spectral theory, limiting properties and long-time dynamics.
      J. Differential Equations 267 (2019), 1423-1466. (with Hoang-Hung Vo)
    6. Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems.
      Commun. Pure Appl. Anal. 2019, 18 (1) : 361-396. (with Xiongxiong Bao and Wenxian Shen)
    7. Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable media.
      European J. Appl. Math. 31 (2020) no. 4, 601-645. (with Wenxian Shen)
    8. Analysis of a diffusive SIR model with seasonality and nonlocal incidence.
      SIAM J. Appl. Math. 79 (2019), no. 6, 2218-2241. (with Zhen Jin, Zhuanzhuan Liu, and Hao Wang)
    9. Integrodifference equations in the presence of climate change: persistence criterion, travelling waves and inside dynamics.
      J. Math. Biol. (2018) 77:1649-1687. (with Mark A. Lewis and Nathan G. Marculis)
      Special issue in memory of Professor Karl Peter Hadeler.
    10. Global dynamics of an infinite-dimensional epidemic model with nonlocal state structures.
      J. Differential Equations 265 (2018), 5262-5296. (with Michael Y. Li and Zhipeng Qiu)
    11. Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media.
      Commun. Pure Appl. Anal. 15 (2016), No. 4, 1193-1213. (with Wenxian Shen)
    12. Regularity of transition fronts in nonlocal dispersal evolution equations.
      J. Dynam. Differential Equations, 29 (2017), no. 3, 1071-1102. (with Wenxian Shen)
    13. Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity.
      J. Differential Equations 262 (2017), no.5, 3390-3430. (with Wenxian Shen)
    14. Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity.
      Discrete Contin. Dyn. Syst. A, 37 (2017), no. 2, 1013-1037. (with Wenxian Shen)
      Special issue in memory of Professor Paul Fife.
    15. Stability, uniqueness and recurrence of generalized traveling waves in time heterogeneous media of ignition type.
      Trans. Amer. Math. Soc. 369 (2017), no. 4, 2573-2613. (with Wenxian Shen)
    16. Transition fronts in time heterogeneous and random media of ignition type.
      J. Differential Equations, 262 (2017), no.1, 454-485. (with Wenxian Shen)
    MathSciNet
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