Department of Mathematical and Statistical Sciences University of Alberta Edmonton, Alberta T6G 2G1, CanadaPhone: (780) 492-0215, Email: yingfei@ualberta.ca Office: CAB 501
PUBLICATIONS AND PREPRINTS
Stochastic Dynamics/Fokker-Planck Equations
Population dynamics under demographic and environmental stochasticity (with Alex Hening, Weiwei Qi and Z. Shen), Ann. Appl. Probab., to appear
Quasi-stationary distributions of absorbed singular diffusion processes in higher dimensions (with A. Hening, W. Qi, and Z. Shen), submitted
Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions (with W. Qi and Z. Shen), Probab. Theory Related Fields, to appear
Concentration of quasi-stationary distributions for one-dimensional diffusions with applications (with Z. Shen and S. Wang), Ann. Inst. Henri Poincaré Probab. Stat., to appear
Transient dynamics of absorbed singular diffusions (with M. Ji, W. Qi, and Z. Shen), J. Dyn. Diff. Equat., No 34 (2022), 3089-3129 (Special Issue in Memory of G. Raugel)
Intermittent synchronization in finite-state random networks under Markov perturbations (with A. Berger, H. Qian and S. Wang), Comm. Math. Phy., Vol 384 (2021), No. 3, 1945-1970
Convergence to periodic probability solutions in Fokker-Planck equations (with M. Ji, W. Qi, and Z. Shen), SIAM J. Math. Ana., Vol 53 No 2 (2021), 1958-1992
Synchronization in discrete-time, denumerable random dynamical systems (with W. Huang, H. Qian, F. Ye, and S. Wang), SIAM J. Appl. Dyn. Sys., Vol 19 No 1 (2020), 233-251
Towards mesoscopic ergodic theory (with W. Qi, Z. Shen, and S. Wang), Sci. China Math., Vol 63 No. 9 (2020), 1853-1876 (Special issue in memory of Professor S. Liao)
Noise-vanishing concentration and limit behaviors of periodic probability solutions (with M. Ji, W. Qi, and Z. Shen), Diff. Integral Equat., Vol 33 No 5-6 (2020), 273-322
Existence of periodic probability solutions to Fokker-Planck equations with applications (with M. Ji, W. Qi, and Z. Shen), J. Funct. Anal., Vol 277 (2019), 108281
Quantitative concentration of stationary measures (with M. Ji and Z. Shen), Physica D, Vol 399 (2019), 73-85
Convergence to equilibrium in Fokker-Planck equations (with M. Ji and Z. Shen), J. Dyn. Diff. Equat., Vol 31 (2019), 1591-1615 (Special Issue in Memory of George R. Sell)
Concentration and limit behaviors of stationary measures (with W. Huang, M. Ji, and Z. Liu), Physica D, Vol 369 (2018), 1-17
Systematic measures of biological networks, Part II: Degeneracy, complexity and robustness (with Y. Li), Comm. Pure Appl. Math., Vol 69 No 10 (2016), 1952-1983
Systematic measures of biological networks, Part I: Invariant measures and entropy (with Y. Li), Comm. Pure Appl. Math., Vol 69 No 9 (2016), 1777-1811
Stochastic stability of measures in gradient systems (with W. Huang, M. Ji, and Z. Liu), Physica D, Vol 314 (2016), 9-17
Steady states of Fokker-Planck equations: III. Degenerate diffusion (with W. Huang, M. Ji, and Z. Liu), J. Dyn. Diff. Equat., Vol 28 No 1 (2016), 127-141
Steady states of Fokker-Planck equations: II. Non-existence (with W. Huang, M. Ji, and Z. Liu), J. Dyn. Diff. Equat., Vol 27 No 3 (2015), 743-762 (Special volume in honor of K. Kirchgaessner)
Steady states of Fokker-Planck equations: I. Existence (with W. Huang, M. Ji, and Z. Liu), J. Dyn. Diff. Equat., Vol 27 No 3 (2015), 721-742 (Special volume in honor of K. Kirchgaessner)
Interior regularity for regional fractional Laplacian (with C. Mou), Comm. Math. Phys., Vol 340 (2015), 233-251
Integral identity and measure estimates for stationary Fokker-Planck equations (with W. Huang, M. Ji, and Z. Liu), Ann. Probab., Vol 43 No 4 (2015), 1712-1730
Bifurcations in a stochastic business cycle model (with D.-W. Huang and H. Wang), Int. J. Bifur. Chaos Appl. Sci. Engrg., Vol 20 No 12 (2010), 4111-4118
Hamiltonian Systems/KAM Theory
Responsive tori in Hamiltonian systems of high order degeneracy - the super-critical case (with W. Si and L. Xu), submitted
Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators (with W. Si and L. Xu), J. Nonl. Sci., Vol 33 (2023), article No 114
Quasi-periodic breathers in granular chains with Hertzian contact potential (with C. Ge and J. Geng), J. Nonl. Sci. Vol 33 (2023), article No 94
Quasi-periodic breathers in Newton's cradle (with C. Ge and J. Geng), J. Math. Phy., Vol 63 No 8 (2022), 082703
Responsive solutions in degenerate oscillators under degenerate perturbations (with W. Si), Annales Henri Poincar\'e, Vol 23 (2022), 333-360
Reducibility of quasi-periodic linear KdV equation (with J. Geng and X. Ren), J. Dyn. Diff. Equat., Vol 34 No 1 (2022), 271-310 (Special Issue in Memory of R. A. Johnson)
Completely degenerate response tori in Hamiltonian systems (with W. Si), Nonlinearity, Vol 33 (2020), 6072-6098
Lower dimension tori of general types in multi-scale Hamiltonian systems (with L. Xu), Nonlinearity, Vol 32 No 6 (2019), 2226-2245
Lower dimensional tori in multi-scale, nearly integrable Hamiltonian systems (with L. Xu and Y. Li), Ann. Henri Poincar\'e, Vol 18 No 1 (2017), 53-83
Poincar\'e-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems (with L. Xu and Y. Li), J. Nonl. Sci., Vol 28 No 1 (2018), 337-369
Viscous stability of Lagrangian tori (with Z. Liang and J. Yan), Ergod. Th. & Dynam. Sys., Vol 34 (2014), 185-210
Littlewood problem for a singular subquadratic potential (with X. Li), Fields Inst. Commun., Vol 64 (2013), 193-209
Invariant tori for Hamiltonian systems with high order proper degeneracy (with Y. Han and Y. Li), Ann. Henri Poincar\'e, Vol 8 No 10} (2010), 1419-1436
Quasi-periodic breathers in Hamiltonian networks of long-range coupling (with J. Geng and J. Viveros), Physica D, Vol 237 (2008), 2866-2892
A KAM theorem for Hamiltonian networks with long ranged couplings (with J. Geng), Nonlinearity, Vol 20 No 6 (2007), 1313-1342
Quasiperiodic dynamics in Bose-Einstein condensates in periodic lattices and superlattices (with M. van Noort, M. A. Porter, and S.-N. Chow), J. Nonl. Sci., Vol 17 No 1 (2007), 59-83
Quasi-periodic solutions in a nonlinear Schr\"odinger equation (with J. Geng), J. Differential Equations, Vol 233 No 2 (2007), 512-542
Nekhoroshev and KAM stabilities in generalized Hamiltonian systems (with Y. Li), J. Dyn. Diff. Equat., Vol 18 No 3 (2006), 577-614
On exact Poisson structures (with X. Zhang), Fields Inst. Commun., Vol 48 (2006), 291-311
Degenerate lower dimensional tori in Hamiltonian systems (with Y. Han and Y. Li), J. Differential Equations, Vol 227 (2006), 670-691
Persistence of lower dimensional tori of general types in Hamiltonian systems (with Y. Li), Trans. Amer. Math. Soc., Vol 357 (2005), 1565-1600
Persistence of hyperbolic tori in Hamiltonian systems (with Y. Li), J. Differential Equations, Vol 208 (2005), 344-387
Quasiperiodic dynamics in Hamiltonian $1{1\over 2}$ degree of freedom systems away from integrability (with S.-N. Chow and M. van Noort), J. Differential Equations, Vol 212 (2005), 366-393
On Poincar\'e - Treshchev tori in Hamiltonian systems (with Y. Li), Proc. Equadiff2003, Dumortier et al (Ed.), World Scientific, 2005, 136-151
A quasi-periodic Poincare's Theorem (with Y. Li), Math. Annalen, Vol 326 (2003), 649-690
Persistence of invariant tori on submanifolds in Hamiltonian systems (with S-N. Chow and Y. Li), J. Nonl. Sci., Vol 12, No 6 (2002), 585-617
Persistence of invariant tori in generalized Hamiltonian systems (with Y. Li), Ergod. Th. & Dynam. Sys., Vol 22 (2002), 1233-1261
Topological Dynamics/Ergodic Theory
Entropy production in dissipative systems (with H. Qian and S. Wang), Proc. Amer. Math. Soc., Vol 147 No 12 (2019), 5209-5225
Asymptotic pairs, stable sets and chaos in positive entropy systems (with W. Huang and L. Xu), J. Funct. Anal., Vol 268 No 4 (2015), 824-846
Dimension of stable sets and scrambled sets (with C. Fang, W. Huang, and P. Zhang), Ergod. Th. & Dynam. Sys., Vol 32 No 2 (2012), 599-628
On Lyapunov exponents of continuous Schr\"{o}dinger cocycles over irrational rotation (with W. Huang), Proc. Amer. Math. Soc., Vol 140 No 9 (2012), 1957-1962
Entropy of dynamical systems with repetition property (with W. Huang and L. Xu), J. Dyn. Diff. Equat. Vol 23 (2011), 683-693
Almost periodically forced circle flows (with W. Huang), J. Fuct. Anal., Vol 257 No 3 (2009), 832-902
A local variational principle of pressures and its applications to equilibrium states (with W. Huang), Israel J. Math., Vol 161 (2007), 29-74
On almost automorphic oscillations, Fields Inst. Commun., Vol 42 (2004), 75-99
On almost automorphic dynamics in symbolic lattices (with A. Berger and S. Siegmund), Ergod. Th. & Dynam. Sys., Vol 24 No 3 (2004), 677-696
Almost automorphic and almost periodic dynamics in skew-product semiflows, Part I: Almost automorphy and almost periodicity; Part II (with W. Shen): Skew-product semiflows; Part III (with W. Shen): Applications to differential equations, Memoirs Amer. Math. Soc., Vol 136 No 647 (1998), 1-93
Topological dynamics and differential equations (with G. R. Sell and W. Shen), Contemp. Math., Vol 215 (1997), 279-297
Ergodicity of minimal sets in scalar parabolic equations (with W. Shen), J. Dyn. Diff. Equat., Vol 8 No 2 (1996), 299-323
On minimal sets of scalar parabolic equations with skew-product structure (with W. Shen), Trans. Amer. Math. Soc., Vol 347 No 11 (1995), 4413-4431
Dynamics of almost periodic scalar parabolic equations (with W. Shen), J. Differential Equations, Vol 122 No 1 (1995), 114-136
Asymptotic almost periodicity of scalar parabolic equations with almost periodic time dependence (with W. Shen), J. Differential Equations, Vol 122 No 2 (1995), 373-397
Singular Perturbation/Math Biology
Relaxation oscillations in predator-prey systems (with S. Ai), J. Dyn. Diff. Equat., to appear (Special issue in memory of P. Brunovsky)
Turing points and relaxation oscillation cycles in simple epidemic models (with M. Li, W. Liu, and C. Shan), SIAM J. Appl. Math., Vol 76 No 2 (2016), 663-687.
Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources (with C. Shan and H. Zhu), J. Differential Equations, Vol 260 No 5 (2016),4339-4365.
Poisson-Nernst-Planck systems for ion flow with a local hard-sphere potential for ion sizes effects (with G. Lin, W. Liu, and M. Zhang), SIAM J. Appl. Dyn. Sys., Vol 12 No 3 (2013), 1613-1648
Quantification of degeneracy in biological systems for characterization of functional interactions between modules (with Y. Li, G. Dwivedi, W. Huang, and M. Kemp), J. Theoret. Biol., Vol 302 (2012), 29-38
Nonlinear oscillations and multiscale dynamics in a closed chemical reaction system (with Y.-F. Li and H. Qian), J. Dyn. Diff. Equat., Vol 22 No 3 (2010), 491-507
Oscillation and multiscale dynamics in a closed chemical reaction system: Second law of thermodynamics and temporal complexity (with Y.-F. Li and H. Qian), J. Chem. Phys. Vol. 129 No. 15 (2008), 154505
Spreading speeds and travelling waves for periodic evolution systems (with X. Liang and X. Zhao), J. Differential Equations, Vol 231 No 1 (2006), 57-77
Malaria epidemics and the sickle-cell gene dynamics (with Z. Feng and H. Zhu), J. Dyn. Diff. Equat., Vol 16 No 4 (2004), 869-896
A metapopulation model with explicit local population dynamics (with Z. Feng, R. Swihart and H. Zhu), J. Math. Biosci. Eng., Vol 1 No 1 (2004) 131-145
Relaxation oscillations in a class of predator-prey systems (with W. Liu and D. Xiao), J. Differential Equations, Vol 188 (2003), 306-331
Travelling wave solutions in a tissue interaction model (with S. Ai and S.-N. Chow), J. Dyn. Diff. Equat., Vol 15 No 2/3 (2003), 517-534
Metapopulation dynamics with migration and local competition (with Z. Feng and H. Zhu), Fields Inst. Commun., Vol 36 (2003), 119-133
Convergence in almost periodic Fisher and Kolmogorov models (with W. Shen), J. Math. Bio., Vol 37 (1998), 84-102
Bifurcation/Invariant Manifolds
Planar analytic nilpotent germs via analytic first integrals (with X. Zhang), preprint
First integrals and normal forms for germs of analytic vector fields (with J. Chen and X. Zhang), J. Differential Equations, Vol 245 (2008), 1167-1184
The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment (with S.-N. Chow and C. Li), Ergod. Th. & Dynam. Sys., Vol 22 (2002), 349-374
Center manifolds for invariant sets of flows (with S.-N. Chow and W. Liu), J. Differential Equations, Vol 168 No 2 (2000), 355-385
Center manifolds of invariant manifolds (with S.-N. Chow and W. Liu), Trans. Amer. Math. Soc., Vol 352 No 11 (2000), 5179-5211
Center manifolds and stability for skew-product flows (with S.-N. Chow), J. Dyn. Diff. Equat., Vol 6 No 4 (1994), 543-582
Hopf bifurcation from non-periodic solutions of differential equations II (with R. A. Johnson), J. Differential Equations, Vol 107 No 2 (1994), 310-340
Generalized integral manifold theorem, J. Differential Equations, Vol 102 No 1 (1993), 153-187
Stability of integral manifold and orbital attraction of quasi-periodic motion, J. Differential Equations, Vol 102 No 2 (1993), 278-322
Elliptic Equations/Variational Method
A variational problem related to phase transition of liquid crystals (with X. Pan), Commun. Appl. Nonl. Anal., Vol 5 No 1 (1998), 1-31
The Melnikov method and elliptic equations with critical exponent (with R. A. Johnson and X. Pan), Indiana Univ. Math. J., Vol 43 No 3 (1994), 1045-1077
Singular solutions of elliptic equation $\Delta u - u + u^p = 0$ (with R. A. Johnson and X. Pan), Annali di Matematic\'a prera ed Appli\'cata (IV), Vol CLXVI (1994), 203-225
Positive solutions of super-critical elliptic equations and asymptotics (with R. A. Johnson and X. Pan), Commun. Partial Diff. Equat., Vol 18 (5&6) (1993), 977-1019
Singular ground states of semi-linear elliptic equations via invariant manifolds theory (with R. A. Johnson and X. Pan), Nonlear Anal., TMA, Vol 20 (1993), 1279-1302