HomCont

HomCont, jointly developed with Alan Champneys (University of Bristol) and Yuri A Kuznetsov (Utrecht University), is a numerical toolbox for homoclinic bifurcation analysis. It is designed for use with AUTO written by Eusebius Doedel (Concordia University). Specifically, HomCont deals with continuation of codimension-one heteroclinic and homoclinic orbits to hyperbolic and saddle-node equilibria, including the detection of many codimension-two singularities and the continuation of these singularities in three or more parameters.


References in zbMATH (referenced in 213 articles , 1 standard article )

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  1. Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.: Analytical approximation of cuspidal loops using a nonlinear time transformation method (2020)
  2. Yagasaki, Kazuyuki; Stachowiak, Tomasz: Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in (\mathbbR^d) for (d=3,4) (2020)
  3. Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.: A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form (2019)
  4. Kalia, Manu; Kuznetsov, Yuri A.; Meijer, Hil G. E.: Homoclinic saddle to saddle-focus transitions in 4D systems (2019)
  5. Lee, Min-Gi; Katsaounis, Theodoros; Tzavaras, Athanasios E.: Localization in adiabatic shear flow via geometric theory of singular perturbations (2019)
  6. Postlethwaite, Claire M.; Rucklidge, Alastair M.: A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors (2019)
  7. Tuwankotta, Johan Matheus; Harjanto, Eric: Strange attractors in a predator-prey system with non-monotonic response function and periodic perturbation (2019)
  8. Amabili, Marco: Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory (2018)
  9. Bujalski, Julia; Dwyer, Grace; Kapitula, Todd; Le, Quang-Nhat; Malvai, Harjasleen; Rosenthal-Kay, Jordan; Ruiter, Joshua: Consensus and clustering in opinion formation on networks (2018)
  10. Burylko, Oleksandr; Mielke, Alexander; Wolfrum, Matthias; Yanchuk, Serhiy: Coexistence of Hamiltonian-like and dissipative dynamics in rings of coupled phase oscillators with skew-symmetric coupling (2018)
  11. Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M.: Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study (2018)
  12. Qin, B. W.; Chung, K. W.; Rodríguez-Luis, A. J.; Belhaq, M.: Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with (D_4) symmetry (2018)
  13. Tao, Molei: Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions (2018)
  14. Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M.: Saddle invariant objects and their global manifolds in a neighborhood of a homoclinic flip bifurcation of case B (2017)
  15. Li, Lin; Lin, Ping; Si, Xinhui; Zheng, Liancun: A numerical study for multiple solutions of a singular boundary value problem arising from laminar flow in a porous pipe with moving wall (2017)
  16. Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan: Modeling and analysis of integrated pest control strategies via impulsive differential equations (2017)
  17. Putelat, T.; Dawes, J. H. P.; Champneys, A. R.: A phase-plane analysis of localized frictional waves (2017)
  18. Stoykov, S.; Margenov, S.: Numerical methods and parallel algorithms for computation of periodic responses of plates (2017)
  19. Verschueren, Nicolas; Champneys, Alan: A model for cell polarization without mass conservation (2017)
  20. Al-Hdaibat, B.; Govaerts, W.; Kuznetsov, Yu. A.; Meijer, H. G. E.: Initialization of homoclinic solutions near Bogdanov-Takens points: Lindstedt-Poincaré compared with regular perturbation method (2016)

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