The applied analysis research group studies mathematical problems arising from physical, chemical, geophysical, biophysical, and materials sciences. These problems often are described by time-dependent partial, ordinary, or integral differential equations, together with sophisticated boundary conditions, interface conditions, and external forcing. Nonlinear dynamical systems offer a geometrical and topological framework for detecting, understanding, and quantifying complex phenomena of these time-dependent differential equations. Partial differential equation theory allows us to correctly formulate well-posed problems and to examine behaviors of solutions, setting the stage for efficient numerical simulations. Nonlocal equations arise from macroscopic modeling of stochastic dynamical systems with Lévy noise and from modeling long-range interactions, and consequently give an understanding of anomalous diffusions.

Faculty with an Interest in Applied Analysis

Fred Weening
Senior Lecturer of Applied Mathematics
Sergey Nadtochiy
Associate Professor of Applied Mathematics
Xiaofan Li
Professor of Applied Mathematics Associate Dean, College of Science
Shuwang Li
Associate Professor of Applied Mathematics
Fred Hickernell
Professor of Applied Mathematics Vice Provost for Research
Igor Cialenco
Director of Graduate Studies of the Department of Applied Mathematics Associate Professor of Applied Mathematics
Tomasz Bielecki
Director, Master of Mathematical Finance Professor of Applied Mathematics Affiliate Professor, Stuart School of Business
Kiah Ong
Senior Lecturer of Applied Mathematics
Arthur Lubin
Associate Professor of Applied Mathematics
Jinqiao Duan
Professor of Applied Mathematics

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.

Recent Publications

  • 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.