Recently I have been working on spatial-temporal Patterns modeled by differential equations. Most of my models are from physical or biological systems. The research methods are mainly related to the following subjects: Applied dynamical systems, Applied DEs(PDE, ODE, DDE, Delayed PDE) Theory, Asymptotic Analysis (asymptotics, perturbation method, boundary layer theory). Besides the theoretical methods, numerical simulations are often used.
Traveling waves and spreading speed are biologically important in species invasion. The determination of spreading speed (pushed or pulled) for a mono-stable system is challenging . Alternatively, for a system with bi-stable nonlinearity, the direction of propagation implies the advantage of one species over the other in the competition for common resource. This propagation direction is also difficult to determine. Currently, with my research group, we are working actively on these problems and some novel contributions have been made.
1. Associate editor of Boundary Value Problems, an open Journal of Springer, Impact factor 1.156.
2. Associate editor of New Trend in Nonlinear Analysis and Application.
Spreading dynamics of a Lotka-Volterra competition model in periodic habitats, J. Differential Equations, 270(2021), 664-693. with H. Wang, H. Wang, PDF
Propagation Speed of the Bistable Traveling Wave to the Lotka-Volterra Competition System in a Periodic Habitat, Journal of Nonlinear Science, 2020, https://doi.org/10.1007/s00332-020-09646-5. With H. Wang PDF
Bistable wave speed of the Lotka-Volterra Competition Model, Journal of Biological Dynamics, 14(1)(2020), 608-620, DOI:10.1080/17513758.2020.1795284. with M. Ma, Q. Zhang, J. Yue PDF
Z. Huang and C. Ou, Speed Determinacy of Traveling Waves to a Stream-Population Model with Allee Effect, SIAM. Appl. Math., 80 (2020), 1820-1840. With Z. Huang. PDF
Speed selection for the wavefronts of the lattice Lotka-Volterra competition system, (With H. Wang Z. Huang) Journal of Differential equations, 2020 PDF
On the conjecture for the pushed wavefront to the diffusive Lotka–Volterra competition model, (With Ahmad Alhasanat), Journal of Mathematical Biology, 2020, PDF
Speed selection for traveling waves of a reaction–diffusion–advection equation in a cylinder, (with Zhe Huang), Journal of Physical D, 2020. PDF
Speed of the Traveling Wave for the Bistable Lotka-Volterra Competition Model, (with M. Ma), Nonlinearity, 2019,.
Propagation Direction of the Bistable Traveling Wavefront for Delayed Non-local Reaction Diffusion Equations, PRSA, 2019 PDF
Linear and Nonlinear Speed Selection for Mono-stable Wave Propagations, (With M. Ma) SIAM Math. Anal. 2019 (pdf)
Stability of Traveling Waves to the Lotka-Volterra Competition Model, (With Ahmad Alhasanat), Complexity, 2019 (pdf)
Minimal-speed selection of traveling waves to the Lotka-Volterra competition model, (With Ahmad Alhasanat), J. Differential Equations. 2019 (pdf)
On a Conjecture Raised by Yuzo Hosono, J Dyn Diff Equa. (With Ahmad Alhasanat) 2019.(pdf)
Existence, Uniqueness, Stability and Bifurcation of Periodic Patterns for a Seasonal Single Phytoplankton Model with Self-shading Effect, with M. Ma, J. Diff Equa. 2017 (pdf)
Selected Previous Publications :