EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 30 / No 5 (October 2025) Wuhan Univ. J. Nat. Sci., 30 5 (2025) 490-496 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 30, Number 5, October 2025
Page(s) 490 - 496
DOI https://doi.org/10.1051/wujns/2025305490
Published online 04 November 2025
  1. Hirsch M W, Smale S, Devaney R L. Differential Equations, Dynamical System, and an Introduction to Chaos[M]. Singapore: Elsevier, 2008. [Google Scholar]
  2. Mei F X. On gradient systems[J]. Mechanics in Engineering, 2012, 34(1): 89-90 (Ch). [Google Scholar]
  3. Mei F X, Wu H B. Gradient Representations of Constrained Mechanical Systems (Volume Ⅰ)[M]. Beijing: Sciences Press, 2016 (Ch). [Google Scholar]
  4. Mei F X, Wu H B. Gradient Representations of Constrained Mechanical Systems (Volume Ⅱ)[M]. Beijing: Sciences Press, 2016 (Ch). [Google Scholar]
  5. Chen X W, Cao Q P, Mei F X. Generalized gradient representation of nonholonomic system of Chetaev's type[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 684-691 (Ch). [Google Scholar]
  6. Chen X W, Zhang Y, Mei F X. Stable generalized Birkhoff systems constructed by using a gradient system with non-symmetrical negative-definite matrix[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 149-153 (Ch). [Google Scholar]
  7. Yin M X, Chen X W. The triple combination gradient representation of Nielsen equation and its stability analysis[J]. Journal of Dynamics and Control, 2023, 21(2): 24-32 (Ch). [Google Scholar]
  8. Tarasov V E. Fractional generalization of gradient and Hamiltonian systems[J]. Journal of Physics A, 2005, 38(26): 5929-5943. [Google Scholar]
  9. Tarasov V E. Fractional generalization of gradient systems[J]. Letters in Mathematical Physics, 2005, 73(1): 49-58. [Google Scholar]
  10. Mei F X, Cui J C, Wu H B. A gradient representation and a fractional gradient representation of Birkhoff system[J]. Transactions of Beijing Institute of Technology, 2012, 32(12): 1298-1230 (Ch). [Google Scholar]
  11. Lou Z M, Mei F X. A second order gradient representation of mechanics system[J]. Acta Physica Sinica, 2012, 61(2): 024502 (Ch). [Google Scholar]
  12. Qi H H, Wang P. Fractional gradient representation of arbitrary order for mechanical system[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 54(8): 2408-2414 (Ch). [Google Scholar]
  13. Wang P. A new fractional gradient representation of Birkhoff systems[J]. Mathematical Problems in Engineering, 2022, 2022: 4493270. [Google Scholar]
  14. Wu H B, Mei F X. A gradient representation of holonomic system in the event space[J]. Acta Physica Sinica, 2015, 64(23): 234501 (Ch). [Google Scholar]
  15. Wang J H, Bao S Y. Combined gradient representations for generalized Birkhoffian systems in event space and its stability analysis[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2021, 38(6): 967-974. [Google Scholar]
  16. Mei F X, Wu H B. Generalized Hamilton system and gradient system[J]. Scientia Sinica -Physica, Mechanica & Astronomica, 2013, 43(4): 538-540 (Ch). [Google Scholar]
  17. Mei F X, Wu H B. Gradient systems and mechanical systems[J]. Acta Mechanica Sinica, 2016, 32(5): 935-940. [Google Scholar]
  18. Mei F X, Wu H B. Bifurcation for the generalized Birkhoffian system[J]. Chinese Physics B, 2015, 24(5): 054501 (Ch). [Google Scholar]
  19. Chen X W, Mei F X. Constrained mechanical systems and gradient systems with strong Lyapunov functions[J]. Mechanics Research Communications, 2016, 76: 91-95. [Google Scholar]
  20. Zhang Y. A gradient representation for a type of non-autonomous Birkhoffian systems[J]. Journal of Suzhou University of Science and Technology (Natural Science Edition), 2015, 32(4): 1-3, 8 (Ch). [Google Scholar]
  21. Guenther R B, Guenther C M, Gottsch J A. The Herglotz Lectures on Contact Transformations and Hamiltonian Systems[M]. Torun: Juliusz Center for Nonlinear Studies, 1996. [Google Scholar]
  22. Georgieva B, Guenther R B. First Noether-type theorem for the generalized variational principle of Herglotz[J]. Topological Methods in Nonlinear Analysis, 2002, 20(2): 261-273. [CrossRef] [MathSciNet] [Google Scholar]
  23. Zhang Y. Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems[J]. Acta Mechenica, 2017, 228(4): 1481-1492. [Google Scholar]
  24. Zhang Y. Recent advances on Herglotz's generalized variational principle of non-conservative dynamics[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2020, 37(1): 13-26. [Google Scholar]
  25. Donchev V. Variational symmetries, conserved quantities and identities for several equations of mathematical physics[J]. Journal of Mathematical Physics, 2014, 55(3): 032901. [Google Scholar]
  26. Lazo M J, Paiva J, Amaral J T S, et al. An action principle for action-dependent Lagrangians: Toward an action principle to non-conservative systems[J]. Journal of Mathematical Physics, 2018, 59(3): 032902. [Google Scholar]
  27. Lazo M J, Paiva J, Frederico G S F. Noether theorem for action-dependent Lagrangian functions: Conservation laws for non-conservative systems[J]. Nonlinear Dynamics, 2019, 97: 1125-1136. [Google Scholar]
  28. Zhang Y. Herglotz's variational problem for non-conservative system with delayed arguments under Lagrangian framework and its Noether's theorem[J]. Symmetry, 2020, 12(5): 845. [NASA ADS] [CrossRef] [Google Scholar]
  29. Xu X X, Zhang Y. A new type of adiabatic invariant for fractional order non-conservative Lagrangian systems[J]. Acta Physica Sinica, 2020, 69(22): 220401 (Ch). [Google Scholar]
  30. Zhang Y. Generalized variational principle of Herglotz type for nonconservative system in phase space and Noether's theorem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1382-1389 (Ch). [Google Scholar]
  31. Zhang Y, Cai J X. Noether's theorem of Herglotz type for nonconservative Hamilton systems in event space[J]. Wuhan University Journal of Natural Sciences, 2021, 26(5): 376-382. [Google Scholar]
  32. Dong X C, Zhang Y. Herglotz-type principle and first integrals for nonholonomic systems in phase space[J]. Acta Mechanica, 2023, 234: 6083-6095. [CrossRef] [MathSciNet] [Google Scholar]
  33. Zhang Y. Noether's theorem for a time-delayed Birkhoffian system of Herglotz type[J]. International Journal of Non-Linear Mechanics, 2018, 101: 36-43. [Google Scholar]
  34. Tian X, Zhang Y. Time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems[J]. Royal Society Open Science, 2019, 6(11): 191248. [Google Scholar]
  35. Ding J J, Zhang Y. Noether's theorem for fractional Birkhoffian system of Herglotz type with time delay[J]. Chaos, Solitons & Fractals, 2020, 138: 109913. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.