Peter Giesl - Publications

For preprints, look at the Sussex Research Online.

Books

  1. Globale Attraktoren für Reaktions-Diffusionsgleichungen auf beschränkten und unbeschränkten Gebieten (Global attractors for reaction-diffusion equations on bounded and unbounded regions). Diploma Thesis, Hamburg, 1997 (in German)
  2. Eine Charakterisierung der Einzugsbereiche von Gleichgewichtspunkten und periodischen Orbits dynamischer Systeme (A characterization of the basins of attraction of equilibria and periodic orbits of dynamical systems). Dissertation, München, 2000 (in German)
  3. Construction of global Lyapunov functions using radial basis functions. Habilitation Thesis, München, 2004.
  4. Construction of Global Lyapunov Functions Using Radial Basis Functions. Lecture Notes in Math. 1904, Springer, 2007.

Review paper

  1. (with Sigurdur Hafstein) Review on Computational Methods for Lyapunov Functions. Discrete Contin. Dyn. Syst. Ser. B 20 No. 8 (2015), 2291-2331.
  2. (with Sigurdur Hafstein and Christoph Kawan) Review on contraction analysis and computation of contraction metrics.  J. Comp. Dyn. 10 No. 1 (2023), 1-47.

Papers (by subject)

Mathematics
    2003
  1. Unbounded Basins of Attraction of Limit Cycles. Acta Math. Univ. Comenian. 72 No. 1 (2003), 81-110.

    2. 2004
  2. Necessary conditions for a limit cycle and its basin of attraction. Nonlinear Anal. 56 No. 5 (2004), 643-677.
  3. On the Basin of Attraction of Limit Cycles in Periodic Differential Equations. Z. Anal. Anwendungen 23 No. 3 (2004), 547-576.
  4. Approximation of domains of attraction and Lyapunov functions using radial basis functions. Proceedings of NOLCOS 2004, vol. II, Stuttgart, Germany, 865-870. 

    5. 2005
  5. The basin of attraction of periodic orbits in nonsmooth differential equations. ZAMM Z. Angew. Math. Mech. 85 No. 2 (2005), 89-104.

    6. 2007
  6. Stepwise calculation of the basin of attraction in dynamical systems using radial basis functions. Algorithms for Approximation, A. Iske and J. Levesly (eds.), Springer-Verlag, Heidelberg, 2007, 113-122.
  7. Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete Contin. Dyn. Syst. 18 No. 2 & 3 (2007), 355-373.
  8. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete Contin. Dyn. Syst. Ser. B 7 No. 1 (2007), 101-124.
  9. On the determination of the basin of attraction of discrete dynamical systems. J. Difference Equ. Appl. 13 No. 6 (2007), 523-546.
  10. (with Holger Wendland) Meshless Collocation: Error Estimates with Application to Dynamical Systems. SIAM J. Numer. Anal. 45 No. 4 (2007), 1723-1741.
  11. On the determination of the basin of attraction of a periodic orbit in two-dimensional systems. J. Math. Anal. Appl. 335 No. 1 (2007), 461-479. doi: 10.1016/j.jmaa.2007.01.069

    12. 2008
  12. (with Martin Rasmussen) Borg's criterion for almost periodic differential equations, Nonlinear Anal. 69 No. 11 (2008), 3722-3733. doi:10.1016/j.na.2007.10.008
  13. Construction of a local and global Lyapunov function using radial basis functions, IMA J. Appl. Math. 73 No. 5 (2008), 782-802. doi: 10.1093/imamat/hxn018
  14. Construction of a local and global Lyapunov Function for Discrete Dynamical Systems using Radial Basis Functions, J. Approx. Theory 153 No. 2 (2008), 184-211. doi:10.1016/j.jat.2008.01.007

    15. 2009
  15. (with Holger Wendland) Approximating the basin of attraction of time-periodic ODEs by meshless collocation. Discrete Contin. Dyn. Syst. 25 No. 4 (2009), 1249-1274. doi:10.3934/dcds.2009.25.1249
  16. On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems. J. Math. Anal. Appl. 354 No. 2 (2009), 606-618. doi:10.1016/j.jmaa.2009.01.027
  17. (with Holger Wendland) Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem. Discrete Contin. Dyn. Syst. Supplement (2009), 259-268.

    18. 2010
  18. (with Sigurdur Hafstein) Existence of piecewise affine Lyapunov functions in two dimensions. J. Math. Anal. Appl. 371 No. 1 (2010), 233-248. doi:10.1016/j.jmaa.2010.05.009

    19. 2011
  19. (with Martin Rasmussen) A note on almost periodic variational equations. Comm. Pure Applied Anal. 10 No. 3 (2011), 983-994. doi:10.3934/cpaa.2011.10.983
  20. Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions. In: Approximation Algorithms for Complex Systems, E. Georgoulis, A. Iske and J. Levesley (eds.), Springer Proceedings in Mathematics, Vol. 3, Springer-Verlag, Berlin, 2011, 205-225.
  21. (with Holger Wendland) Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems. Nonlinear Anal. 74 No. 10 (2011), 3191-3203.

    22. 2012
  22. (with Sigurdur Hafstein) Construction of Lyapunov functions for nonlinear planar systems by linear programming. J. Math. Anal. Appl. 388 No. 1 (2012), 463-479. doi: 10.1016/j.jmaa.2011.10.047
  23. (with Holger Wendland) Numerical determination of the basin of attraction for asymptotically autonomous dynamical systems. Nonlinear Anal. 75 No. 5 (2012), 2823-2840.
  24. (with Sigurdur Hafstein) Existence of piecewise linear Lyapunov functions in arbitrary dimensions. Discrete Contin. Dyn. Syst. 32 No. 10 (2012), 3539-3565.
  25. (with Martin Rasmussen) Areas of attraction for nonautonomous differential equations on finite time intervals. J. Math. Anal. Appl. 390 No. 1 (2012), 27-46.
  26. Construction of a finite-time Lyapunov function by Meshless Collocation. Discrete Contin. Dyn. Syst. Ser. B 17 No. 7 (2012), 2387-2412.

    27. 2013
  27. (with Sigurdur Hafstein) Construction of a CPA contraction metric for periodic orbits using semidefinite optimization. Nonlinear Anal. 86 (2013), 114-134.
  28. (with Sigurdur Hafstein) Local Lyapunov Functions for Periodic and Finite-Time ODEs. In: Recent Trends in Dynamical Systems, A. Johann, H.-P. Kruse, F. Rupp and S. Schmitz (eds.), Springer Proceedings in Mathematics & Statistics, Vol. 35, Springer-Verlag, Berlin, 2013, 125-152.

    29. 2014
  29. (with Sigurdur Hafstein) Revised CPA method to compute Lyapunov functions for nonlinear systems. J. Math. Anal. Appl. 410 (2014), 292-306.
  30. (with Sigurdur Hafstein) Computation of Lyapunov functions for nonlinear discrete systems by linear programming. J. Difference Equ. Appl. 20 (2014), 610-640.
  31. (with Sigurdur Hafstein) Implementation of a Simplicial Fan Triangulation for the CPA Method to compute Lyapunov Functions. In: Proceedings of the 2014 American Control Conference, Portland (OR), USA, 2014, no. 0202, pp. 2989-2994.
  32. (with Johann Björnsson and Sigurdur Hafstein) Algorithmic verification of approximations to complete Lyapunov functions. In: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), Groningen, The Netherlands, 2014, no. 0180, pp. 1181-1188.
  33. (with Johann Björnsson, Sigurdur Hafstein, Chris Kellett and Huijuan Li) Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction. In: Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, California, USA, December 15-17, 2014, pp. 5506-5511.

    34. 2015
  34. (with Johann Björnsson, Sigurdur Hafstein and Chris Kellett) Computation of Lyapunov functions for Systems with Multiple Attractors. Discrete Contin. Dyn. Syst. 35 (2015), 4019-4039.
  35. (with Najla Mohammed) Grid refinement in the construction of Lyapunov functions using Radial Basis Functions. Discrete Contin. Dyn. Syst. Ser. B 20 No. 8 (2015), 2453-2476.
  36. Converse theorems on contraction metrics for an equilibrium. J. Math. Anal. Appl. 424 (2015), 1380-1403.
  37. (with Sigurdur Hafstein) Computation and Verification of Lyapunov functions. SIAM J. Appl. Dyn. Syst. 14 No. 4 (2015), 1663-1698.

    38. 2016
  38. (with James McMichen) Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation. Journal of Computational Dynamics 3 No. 2 (2016), 191-210.

    39. 2017
  39. (with Carlos Argaez Garcia, Sigurdur Hafstein) Analysing Dynamical Systems - Towards Computing Complete Lyapunov Functions. In: Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, 2017, pp. 134-144.
  40. (with Carlos Argaez Garcia, Sigurdur Hafstein) Wendland Functions - A C++ Code to Compute Them. In: Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, 2017, pp. 323-330.
  41. Computation of a Finsler-Lyapunov function using meshless collocation. In: Mathematical and Numerical Aspects of Dynamical System Analysis, (Eds.) J. Awrejcewicz, M. Kazmierczak, J. Mrozowski, P. Olejnik, DAB&M of TUL Press, Lodz, Poland 2017, pp. 193-204.

    42. 2018
  42. (with Skuli Gudmundsson, Sigurdur Hafstein, Enrico Scalas) Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete Contin. Dyn. Syst. Ser. B 23 No. 2 (2018), 939-956.
  43. (with James McMichen) Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation. Discrete Contin. Dyn. Syst. Ser. B 23 No. 4 (2018), 1835-1850.
  44. (with Carlos Argaez Garcia, Sigurdur Hafstein) Computational Approach for Complete Lyapunov Functions. In: Dynamical Systems in Theoretical Perspective, Springer Proceedings in Mathematics and Statistics 248, J. Awrejcewicz (ed.), pages 1-11 (2018).
  45. (with Carlos Argaez Garcia, Sigurdur Hafstein) Iterative construction of complete Lyapunov functions. In: Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, pages 211-222 (2018).
  46. (with Najla Mohammed) Combination of refinement and verification for the construction of Lyapunov functions using Radial Basis Functions. In: Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE, pages 569-578 (2018).
  47. (with Carlos Argaez Garcia, Sigurdur Hafstein, Holger Wendland) Construction of a complete Lyapunov function using quadratic programming. In: Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE, pages 560-568 (2018).
  48. (with Hjortur Björnsson, Skuli Gudmundsson, Sigurdur Hafstein) Local Lyapunov functions for nonlinear stochastic differential equations by linearization. In: Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE, pages 579-586 (2018).
  49. (with Carlos Argaez Garcia, Sigurdur Hafstein) Computation of complete Lyapunov functions for three-dimensional systems. In: Proceedings of the 57rd IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, pages 4059-4064 (2018).
  50. (with Holger Wendland) Kernel-based Discretisation for Solving Matrix-Valued PDEs. SIAM J. Numer. Anal. 56 No. 6 (2018), 3386-3406.

    51. 2019
  51. (with Carlos Argaez Garcia and Sigurdur Hafstein) Complete Lyapunov Functions: Computation and Applications. In: Simulation and Modeling Methodologies, Technologies and Applications Series: Advances in Intelligent Systems and Computing 873, M. Obaidat, T. Oren, and F. De Rango (eds.), Springer, pages 200-221 (2019).
  52. (with Carlos Argaez Garcia and Sigurdur Hafstein) Improved estimation of the chain-recurrent set. In: Proceedings of the 18th European Control Conference (ECC), Napoli, Italy, pages 1622-1627 (2019).
  53. Construction of Finsler-Lyapunov functions with meshless collocation.  ZAMM - Journal of Applied Mathematics and Mechanics Z. Angew. Math. Mech. 99 No. 4 (2019), e201800141.
  54. (with Pascal Stiefenhofer) Economic Periodic Orbits: A Theory of Exponential Asymptotic Stability. Nonlinear Analysis and Differential Equations 7 No. 1 (2019), 9-16.
  55. Converse theorem on a global contraction metric for a periodic orbit. Discrete Contin. Dyn. Syst. 39 No. 9 (2019), 5339-5363.
  56. (with Pascal Stiefenhofer) A Global Stability Theory of Nonsmooth Periodic Orbits: Example I. Applied Mathematical Sciences 13 No. 11 (2019), 511-520.
  57. (with Pascal Stiefenhofer) Local stability theory of nonsmooth periodic orbits: example II. Applied Mathematical Sciences 13 No. 11 (2019), 521-531.
  58. (with Pascal Stiefenhofer) Switching Regimes in Economics: The Contraction Mapping and the ω-Limit Set. Applied Mathematics 10 (2019), 513-520.
  59. (with Holger Wendland) Construction of a Contraction Metric by Meshless Collocation. Discrete Contin. Dyn. Syst. Ser. B 24 No. 8 (2019), 3843-3863.
  60. (with Najla Mohammed) Verification Estimates for the Construction of Lyapunov Functions using Mesh-free Collocation. Discrete Contin. Dyn. Syst. Ser. B 24 No. 9 (2019), 4955-4981.
  61. (with Hjortur Björnsson, Skuli Gudmundsson, Sigurdur Hafstein and Enrico Scalas) Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete Contin. Dyn. Syst. Ser. B 24 No. 8 (2019), 4247-4269.
  62. (with Jürgen Giesl and Marcel Hark) Computing Expected Runtimes for Constant Probability Programs. In: Proceedings of CADE Conference on Automated Deduction, Natal, Brasil pages 266-283 (2019).
  63. (with Carlos Argaez Garcia and Sigurdur Hafstein) Clustering algorithm for generalized recurrences using complete Lyapunov functions. In: Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics (ICINCO), pages 138-146 (2019).
  64. (with Carlos Argaez Garcia and Sigurdur Hafstein) Critical tolerance evolution: Classification of the chain-recurrent set. In: Proceedings of the 15th International Conference DSTA Dynamical Systems - Theory and Applications, Lodz, Poland, pages 21-32 (2019).
  65. (with Carlos Argaez Garcia and Sigurdur Hafstein) Middle Point Reduction of the Chain-recurrent Set. In: Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, pages 141-152 (2019).
  66. (with Carlos Argaez Garcia, Jean-Claude Berthet, Hjortur Björnsson and Sigurdur Hafstein) LyapXool - a program to compute complete Lyapunov functions. SoftwareX 10 (2019) 100325. https://doi.org/10.1016/j.softx.2019.100325
  67. Computation of a contraction metric for a periodic orbit. SIAM J. Appl. Dyn. Syst. 18 No. 3 (2019), 1536-1564.

    68. 2020
  68. (with Carlos Argaez Garcia and Sigurdur Hafstein) Iterative Construction of Complete Lyapunov Functions: Analysis of Algorithm Efficiency. In: Simulation and Modeling Methodologies, Technologies and Applications, M. Obaidat, T. Oren, and F. De Rango (eds.), Springer, pages 83-100 (2020).
  69. (with Sigurdur Albertsson, Sigurdur Hafstein and Skuli Gudmundsson) Simplicial complex with approximate rotational symmetry: A general class of simplicial complexes. J. Comput. Appl. Math. 363 (2020), 413-425.
  70. (with Boumediene Hamzi, Martin Rasmussen and Kevin Webster) Approximation of Lyapunov Functions from Noisy Data. J. Comp. Dyn. 7 No. 1 (2020), 57-81.
  71. (with Conor Osborne and Sigurdur Hafstein) Automatic determination of connected sublevel sets of CPA Lyapunov functions. SIAM J. Appl. Dyn. Syst. 19 No. 2 (2020), 1029-1056.
  72. (with Carlos Argaez Garcia and Sigurdur Hafstein) Update (2.0) to LyapXool: Eigenpairs and new classification methods. SoftwareX 12 (2020) 100616. https://doi.org/10.1016/j.softx.2020.100616
  73. (with Carlos Argaez Garcia, Sigurdur Hafstein) Evaluation of Lyapunov Function Candidates Through Averaging Iterations. In: Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics - ICINCO, pages 734-744 (2020).

    74. 2021
  74. (with Sigurdur Hafstein) System Specific Triangulations for the Construction of CPA Lyapunov Functions. Discrete Contin. Dyn. Syst. Ser. B 26 No. 12 (2021), 6027-6046.
  75. On a matrix-valued PDE characterizing a contraction metric for a periodic orbit. Discrete Contin. Dyn. Syst. Ser. B 26 No. 9 (2021), 4839-4865.
  76. (with Sigurdur Hafstein and Iman Mehrabinezhad) Computation and Verification of Contraction Metrics for Equilibria. J. Comput. Appl. Math. 390 (2021), 113332.
  77. (with Carlos Argaez Garcia and Sigurdur Hafstein) Complete Lyapunov Functions: Determination of the Chain-recurrent set using the Gradient. In: Simulation and Modeling Methodologies, Technologies and Applications, M. Obaidat, T. Oren, and F. De Rango (eds.), Springer, pages 104-121 (2021).
  78. (with Sigurdur Hafstein and Iman Mehrabinezhad) Computing Contraction Metrics for three-dimensional systems. Ifac-PapersOnLine 54 (2021), 297-303.
  79. (with Sigurdur Hafstein and Iman Mehrabinezhad) Computing Contraction Metrics: Comparison of Different Implementations. Ifac-PapersOnLine 54 (2021), 310-316.
  80. (with Carlos Argaez Garcia, Sigurdur Hafstein and Holger Wendland) Minimization with differential inequality constraints applied to complete Lyapunov functions. Math. Comp. 90 (2021), 2137-2160.
  81. (with Carlos Argaez Garcia, Sigurdur Hafstein and Zachary Langhorne) Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete Contin. Dyn. Syst. Ser. B 26 (2021), 299-336.
  82. (with Sigurdur Hafstein) Uniformly regular triangulations for parameterizing Lyapunov functions. In: Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO, pages 549-557 (2021).
  83. (with Sigurdur Hafstein and Iman Mehrabinezhad) Computation and verification of contraction metrics for periodic orbits. J. Math. Anal. Appl. 503 (2021), Article 125309.
  84. (with Sigurdur Hafstein and Iman Mehrabinezhad) Robustness of Contraction metrics computed by Radial Basis Functions. In: Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO, pages 592-599 (2021).
  85. (with Carlos Argaez Garcia and Sigurdur Hafstein) Comparison of different Radial Basis Functions in Dynamical Systems. In: Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH, pages 394-405 (2021).
  86. (with Christoph Kawan and Sigurdur Hafstein) ResEntSG: Restoration Entropy Estimation for Dynamical Systems via Riemannian Metric Optimization. SoftwareX 15 (2021), Article 100743.
  87. (with Christoph Kawan and Sigurdur Hafstein) A subgradient algorithm for data-rate optimization in the remote state estimation problem. SIAM J. Appl. Dyn. Syst. 20 No. 4 (2021), 2142-2173.

    88. 2022
  88. (with Carlos Argaez Garcia and Sigurdur Hafstein) Statistical Analysis of an Iterative Algorithm Class for Dynamical Systems. In: Advances in Nonlinear Dynamics, NODYCON Conference Proceedings Series. W. Lacarbonara, B. Balachandran, M. Leamy, J. Ma, J., J. Tenreiro Machado, G. Stepan (eds.), Springer, pages 453-464 (2022).
  89. (with Carlos Argaez Garcia and Sigurdur Hafstein) WendlandXool: Simplified C Code to Compute Wendland Functions. In: Advances in Nonlinear Dynamics, NODYCON Conference Proceedings Series. W. Lacarbonara, B. Balachandran, M. Leamy, J. Ma, J., J. Tenreiro Machado, G. Stepan (eds.), Springer, pages 465-474 (2022).
  90. (with Sigurdur Hafstein and Stefan Suhr) Existence of complete Lyapunov functions with prescribed orbital derivative. Discrete Contin. Dyn. Syst. Ser. B 20 No. 11 (2022), 6927-6941.
  91. (with Sigurdur Hafstein and Iman Mehrabinezhad) Robustness of numerically computed contraction metrics. (extended version) SN Comput. Sci. 3 257 (2022).
  92. (with Mauricio Louzeiro, Christoph Kawan, Sigurdur Hafstein and Jinyun Yuan) A Projected Subgradient Method for the Computation of Adapted Metrics.   SIAM J. Appl. Dyn. Syst. 21 No. 4 (2022), 2610-2641.
  93. (with Carlos Argaez Garcia and Sigurdur Hafstein) Eigenpairs for the analysis of complete Lyapunov functions. Complexity 2022, Article ID 3160052, https://doi.org/10.1155/2022/3160052

    94. 2023
  94. (with Stefania Andersen and Sigurdur Hafstein) Common Lyapunov functions for switched linear systems: Linear Programming based approach. IEEE Control Systems Letters 7 (2023), 901-906.
  95. (with Najla Mohammed) Modified refinement algorithm to construct Lyapunov functions using meshless collocation.   J. Comp. Dyn. 10 No. 1 (2023), 127-151.
  96. (with Sigurdur Hafstein, Magnea Haraldsdottir, Christoph Kawan and David Thorsteinsson) Subgradient Algorithm for computing Contraction Metrics for Equilibria. J. Comp. Dyn. 10 No. 2 (2023), 281-303.
  97. (with Sigurdur Hafstein) Triangulations and Error Estimates for Interpolating Lyapunov Functions. SN Computer Science (2023) 4:364
  98. (with Sigurdur Hafstein and Iman Mehrabinezhad) Contraction Metric by Numerical Integration and Quadrature: Uniform Error Estimate. In: Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO), Vol. 1, pages 196-205 (2023).
  99. (with Sigurdur Hafstein and Iman Mehrabinezhad) Positively Invariant Sets for ODEs and numerical Integration. In: Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO), Vol. 1, pages 44-53 (2023).

    100. 2024
  100. (with Sareena Pokkakkillath) Construction of Contraction Metrics for Discrete-time Dynamical Systems using Meshfree Collocation. Discrete Contin. Dyn. Syst. Ser. B
    101. 29 No. 4 (2024), 2043-2071.
  101. (with Sigurdur Hafstein and Iman Mehrabinezhad) Contraction Metric Computation using numerical Integration and Quadrature. Discrete Contin. Dyn. Syst. Ser. B
    102. 29 No. 6 (2024), 2610-2632.

    submitted
  102. (with Sigurdur Hafstein) Lyapunov functions by interpolating numerical quadrature: proof of convergence. submitted
  103. (with Sigurdur Hafstein, Stefan Suhr and Holger Wendland) Minimization with differential inequality and equality constraints applied to complete Lyapunov functions. submitted
  104. (with Jordan Boote and Stefan Suhr) Construction of a contraction metric for non-smooth time-periodic systems. submitted
  105. (with Sigurdur Hafstein) Construction of a contraction metric for time-periodic systems using meshless collocation. submitted
  106. (with Sigurdur Hafstein and Sareena Pokkakkillath) Piecewise Quadratic Lyapunov Functions for Stochastic Differential Equations by Linear Programming. submitted
  107. (with Sigurdur Hafstein and Iman Mehrabinezhad) Positively invariant sets for ODEs and numerical solvers. submitted
Mathematics and Biomechanics
  1. Selbststabilisierung menschlicher Bewegung (Self-stabilization of human movement). Thesis paper in: Hanns Martin Schleyer-Stiftung, Heinz Nixdorf Stiftung, TU München: Ein Almanach junger Wissenschaftler. hrsg. zum I. Kongress Junge Naturwissenschaft und Praxis, München, 11.-13. Juni 2003, 58-59 (in German)
  2. The optimal elbow angle for acrobatics - stability analysis of the elbow with a load. PAMM Proc. Appl. Math. Mech. 3 (2003), 68-71.
  3. (with Dorothea Meisel, Jürgen Scheurle and Heiko Wagner) Stability Analysis of the Elbow with a Load. Journal of Theoretical Biology 228 No. 1 (2004), 115-125.
  4. (with Heiko Wagner) Self-stability in Biological Systems - Studies based on Biomechanical Models, in: Fast Motions in Biomechanics and Robotics, M. Diehl and K. Mombaur (eds.), Springer-Verlag, LNCIS 340 (2006),  403-410.
  5. (with Heiko Wagner) On the Determination of the Basin of Attraction for Stationary and Periodic Movements, in: Fast Motions in Biomechanics and Robotics, M. Diehl and K. Mombaur (eds.), Springer-Verlag, LNCIS 340 (2006), 147-166.
  6. (with Heiko Wagner) Lyapunov functions and the basin of attraction for a single-joint muscle-skeletal model. J. Math. Biol. 54 No. 4 (2007), 453-464. doi: 10.1007/s00285-006-0052-8
  7. (with Heiko Wagner and Reinhard Blickhan) Musculoskeletal Stabilization of the Elbow - Complex or Real. Journal of Mechanics in Medicine and Biology 7 No. 3 (2007), 275-296.
  8. (with Heiko Wagner) Mathematical Stability Analysis in Biomechanical Applications, in: Mathematical Biology Research Trends, L. Wilson (ed.), Nova Science Publishers, 2008, 261-273.
  9. (with Katja Mombaur and Heiko Wagner) Stability Optimization of Juggling, in: Modeling, Simulation and Optimization of Complex Processes, H. G. Bock, E. Kostina, X. P. Hoang, R. Rannacher (eds.), Springer, Berlin, 2008, 419-432. doi: 10.1007/978-3-540-79409-7
  10. (with Michael Ernst and Heiko Wagner) Einzugsbereiche eines menschlichen Armmodells: Eine Analyse basierend auf Lyapunovfunktionen (Basins of attraction of a human arm model: analysis based on Lyapunov functions), in: BZB (Beiträge zur Bewegungswissenschaft) Band 1, Th. Ertelt (ed.), Verlag Dr. Kovac, Hamburg, 2010, 97-134. (in German)
  11. (with Pascal Stiefenhofer and Heiko Wagner) A System of Inverted Nonsmooth Pendula: Modelling an Elderly Person Stepping over an Obstacle. Nonlinear Analysis and Differential Equations 7 No. 1 (2019), 17-32.
Mathematics and Music
  1. Stimmung und Kettenbrüche (Tuning and continued fractions), in: Mikrotöne und mehr. Auf György Ligetis Hamburger Pfaden, Manfred Stahnke (Hrsg.), von Bockel Verlag, Hamburg, 2005, 243-263. (in German)
  2. The Flow of Harmony as a Dynamical System, in Mathematics and Computation in Music. First International Conference 2007, T. Klouche and T. Noll (eds.), CCIS 37, Springer, 2009, 117-123.
  3. Intervalle und Stimmungssysteme, in: Denk(t)räume, Band 4 Mathematik und Musik (2009) 11-15 (in German)
Music theory (all in German)
  1. Von Stimmführungsvorgängen zur Harmonik. Eine Anwendung der Clausellehre auf Wagners "Tristan und Isolde", in: Die Musikforschung 52 (1999), 403-436 (in German)
  2. Von Stimmführungsvorgängen zu Kleinterzzirkeln. Eine Deutung der Teufelsmühle durch die Clausellehre, in: Die Musikforschung 54 (2001), 378-399 (in German)
  3. Zur melodischen Verwendung des Zweiten Modus in Messiaens Subtilité des Corps Glorieux, in: Musik, Wissenschaft und ihre Vermittlung; Bericht über die Internationale Musikwissenschaftliche Tagung Hannover 2001, Arnfried Edler & Sabine Meine (hrsg.). Publikationen der Hochschule für Musik und Theater Hannover, Band 12. Wißner, Augsburg, 2002, 259-264 (in German)
  4. Der Tristan-Akkord aus der Sicht der Clausellehre, in: Der "Komponist" Richard Wagner im Blick der aktuellen Musikwissenschaft, Symposion Würzburg 2000, Ulrich Konrad & Egon Voss (hrsg.). Breitkopf & Härtel, Wiesbaden, 2003, 117-125 (in German)

Research

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