Department of Applied Mathematics
Faculty with an Interest in Applied Analysis
Recent Research Grants
- NSF DMS-1620449 (PI X. Li and Co-PI J. Duan): Theoretical and Numerical Studies of Nonlocal Equations Derived from Stochastic Differential Equations with Lévy Noises, 2016-2020.
- NSF DMS-1642545 (PI J. Duan and Co-PI X. Li): CBMS Conference: Nonlocal Dynamics — Theory, Computation and Applications, 2017-2018.
- NSF DMS-1025422 (PI J. Duan): CMG Collaborative Research: Mathematical Modeling by Bridging Primitive and Boussinesq Equations, 2010-2014.
- Z. Cheng, J. Duan, and L. Wang. Most Probable Dynamics of Some Non-Linear Systems under Noisy Fluctuations. Communications in Nonlinear Science and Numerical Simulation (2016), Vol. 30, Issue 1-3, pp. 108-114.
- T. Gao and J. Duan. Quantifying Model Uncertainty in Dynamical Systems Driven by Non-Gaussian Lévy Stable Noise with Observations on Mean Exit Time or Escape Probability. Communications in Nonlinear Science and Numerical Simulation (2016), Vol. 39, pp. 1-6.
- T. Gao, J. Duan, X. Kan, and Z. Cheng. Dynamical Inference for Transitions in Stochastic Systems with Alpha-Stable Lévy Noise. Journal of Physics A: Mathematical and Theoretical (2016), Vol. 49, No. 19, Article Number 294002.
- T. Gao, J. Duan, and X. Li. Fokker-Planck Equations for Stochastic Dynamical Systems with Symmetric Lévy Motions. Applied Mathematics and Computation (2016), Vol. 278, pp. 1-20.
- G. Lv, J. Duan, H. Gao, and J.-L.Wu. On a Stochastic Nonlocal Conservation Law in a Bounded Domain. Bulletin des Sciences Mathématiques (2016), Vol. 140, Issue 6, pp. 718 -746.
- H. Qiao and J. Duan. Stationary Measures for Stochastic Differential Equations with Jumps. Stochastics: An International Journal of Probability and Stochastic Processes (2016), Vol. 88, Issue 6, pp. 864-883.
- L. Serdukova, Y. Zheng, J. Duan, and J. Kurths. Stochastic Basins of Attraction for Metastable States. Chaos: An Interdisciplinary Journal of Nonlinear Science (2016), Vol. 26, Issue 7, Article Number 073117.
- T. Wang, J. Duan, and T. Liu. Competition Promotes the Persistence of Populations in Ecosystems. Nature - Scientific Reports (2016), Vol. 6, Article Number 30477.
- Y. Zheng, J. Duan, L. Serdukova, and J. Kurths. Transitions in a Genetic Transcriptional Regulatory System under Lévy Motion. Nature - Scientific Reports (2016), Vol. 6, Article Number 29274.
- G. Lv and J. Duan. Impacts of Noise on a Class of Partial Differential Equations. Journal of Differential Equations (2015). Vol. 258, Issue 6, pp. 2196-2220.
- H. Qiao and J. Duan. Nonlinear Filtering of Stochastic Dynamical Systems with Lévy Noises. Advances in Applied Probability (2015), Vol. 47, No. 3, pp. 902-918.
- J. Ren, J. Duan, and C. K. R. T. Jones. Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty. Journal of Dynamics and Differential Equations (2015), Vol. 27, Issue 3, pp. 961-979.
- J. Ren, J. Duan, and X. Wang. A Parameter Estimation Method Based on Random Slow Manifolds. Applied Mathematical Modelling (2015), Vol. 39, Issue 13, pp. 3721-3732.
- W. Zou, D. V. Senthilkumar, R. Nagao, I. Z. Kiss, Y. Tang, A. Koseska, J. Duan, and J. Kurths. Restoration of Rhythmicity in Diffusively Coupled Dynamical Networks. Nature Communications (2015), Vol. 6, Article Number 7709.