(A) Chaos and Predictability:

  1. Shen, B.-W.*, 2020: Homoclinic Orbits and Solitary Waves within the non-dissipative Lorenz Model and KdV Equation. International Journal of Bifurcation and Chaos. 30. 2050257-1-15. DOI:10.1142/S0218127420502570.

  2. Shen, B.-W.*, R. A. Pielke Sr., X. Zeng, J.-J. Baik,  S. Faghih-Naini#, J. Cui#, and R. Atlas, 2021: Is Weather Chaotic? Coexistence of Chaos and Order within a Generalized Lorenz Model. Bulletin of the American Meteorological Society, 102(1), E148-E158. Retrieved Jan 29, 2021, from https://journals.ametsoc.org/view/journals/bams/102/1/BAMS-D-19-0165.1.xml

  3. Shen, B.-W.*, 2021: Solitary Waves, Homoclinic Orbits, and Nonlinear Oscillations within the non-dissipative Lorenz Model, the inviscid Pedlosky Model, and the KdV Equation. In: Christos H. Skiadas, Yiannis Dimotikalis (eds) The 13th Chaos International Conference CHAOS 2020. Springer Proceedings in Complexity. Springer, Cham. http://doi.org/10.13140/RG.2.2.26813.90089. (accepted)

  4. Shen, B.-W.*, R. A. Pielke Sr., X. Zeng, J.-J. Baik, S. Faghih-Naini, J. Cui, R. Atlas, T.A. Reyes, 2021:  Is Weather Chaotic? Coexisting Chaotic and Non-Chaotic Attractors within Lorenz Models. In: Christos H. Skiadas, Yiannis Dimotikalis (eds) The 13th Chaos International Conference CHAOS 2020. Springer Proceedings in Complexity. Springer, Cham. (accepted) (pdf) 

  5. Shen, B.-W., 2019a: Aggregated Negative Feedback in a Generalized Lorenz Model. International Journal of Bifurcation and Chaos. Vol. 29, No. 3 (2019) 1950037 (20 pages). https://doi.org/10.1142/S0218127419500378.
  6. Shen, B.-W.*, 2019b: On the Predictability of 30-day Global Mesoscale Simulations of Multiple African Easterly Waves during Summer 2006: A View with a Generalized Lorenz Model. Geosciences 2019, 9(7), 281; https://doi.org/10.3390/geosciences9070281 

  7. Shen, B.-W.*, T. Reyes#, and S.  Faghih-Naini#, 2018: Coexistence of Chaotic and Non-Chaotic Orbits in a New Nine-Dimensional Lorenz Model.11th Chaotic Modeling and Simulation International Conference  (Editors: C. H. Skiadas and I. Lubashevsky), Springer Proceedings in Complexity, https://www.springer.com/us/book/9783030152963  (in press, to appear in August, 2019) (slides) (pdf)

  8. Reyes, T.# and B.-W. Shen*, 2019a:  A Recurrence Analysis of Chaotic and Non-Chaotic Solutions within a Generalized Nine-Dimensional Lorenz Model. Chaos, Solitons & Fractals. 125 (2019), 1-12. https://doi.org/10.1016/j.chaos.2019.05.003

  9. Shen, B.-W., R. A. Pielke Sr., X. Zeng, S. Faghih-Naini, C.-L. Shie, R. Atlas, J.-J. Baik, and T. A. L. Reyes, 2018: Butterfly Effects of the First and Second Kinds: New Insights Revealed by High-dimensional Lorenz Models.  The 11th Chaos International Conference (CHAOS2018), Rome, Italy, June 5-8, 2018.  https://doi.org/10.13140/RG.2.2.16647.70564 

  10. Shen, B.-W., 2018: On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop. Tellus A: 2018, 70, 1471912, https://doi.org/10.1080/16000870.2018.1471912.  (pdf)

  11. Faghih-Naini, S. and B.-W. Shen, 2018: Quasi-periodic orbits in the five-dimensional non-dissipative Lorenz model: the role of the extended nonlinear feedback loop. International Journal of Bifurcation and Chaos, Vol. 28, No. 6 (2018) 1850072 (20 pages).DOI: 10.1142/S0218127418500724.  (IJBC is ranked 6th out of 111 in the Multidisciplinary category) (gallery) (pdf) 

  12. Shen, B.-W. and  S. Faghih-Naini, 2017: On recurrent solutions within high-dimensional non-dissipative Lorenz models: the role of the nonlinear feedback loop. The 10th Chaos Modeling and Simulation International Conference (CHAOS2017), Barcelona, Spain, 30 May - 2 June, 2017.   (slides) (pdf)

  13. Shen, B.-W., 2017: On an extension of the nonlinear feedback loop in a nine-dimensional Lorenz model. Chaotic Modeling and Simulation (CMSIM), 2: 147–157, 2017. (pdf)

  14. Shen, B.-W., 2016: Hierarchical scale dependence associated with the extension of the  nonlinear feedback loop in a seven-dimensional Lorenz model. Nonlin. Processes Geophys., 23, 189-203, doi:10.5194/npg-23-189-2016, 2016. (link) (pdf)

  15. Shen, B.-W., 2015b: Nonlinear Feedback in a Six-dimensional Lorenz Model. Impact of an additional heating term. Nonlin. Processes Geophys., 22, 749-764, doi:10.5194/npg-22-749-2015, 2015. (link) (pdf)

  16. Shen, B.-W., 2015a: Parameterization of Negative Nonlinear Feedback using a Five-dimensional Lorenz Model. Fractal Geometry and Nonlinear Anal in Med and Bio. 1, 33-41, doi: 10.15761/FGNAMB.1000109 (pdf)

  17. Shen, B.-W., 2014b: On the nonlinear feedback loop and energy cycle of the non-dissipative Lorenz model. Nonlin. Processes Geophys. Discuss., 1, 519-541, doi:10.5194/npgd-1-519-2014, 2014. (pdf)

  18. Shen, B.-W., 2014a: Nonlinear Feedback in a Five-dimensional Lorenz Model. J. of Atmos. Sci., 71, 1701–1723. doi:http://dx.doi.org/10.1175/JAS-D-13-0223.1 (pdf) 

  19. Shen, B.-W., and N.-H. Lin, 1995: A Theoretical Study of the Effects of an Isolated Mountain on Particle Deposition. J. of Atmos. Sci., 23, Taipei, Taiwan (in Chinese), 237-264.