AUTO is a software for continuation and bifurcation problems in ordinary differential equations, originally developed by Eusebius Doedel, with subsequent major contribution by several people, including Alan Champneys, Fabio Dercole, Thomas Fairgrieve, Yuri Kuznetsov, Bart Oldeman, Randy Paffenroth, Bjorn Sandstede, Xianjun Wang, and Chenghai Zhang. AUTO can do a limited bifurcation analysis of algebraic systems of the form f(u,p) = 0, f,u in Rn and of systems of ordinary differential equations of the form u’(t) = f(u(t),p), f,u in Rn subject to initial conditions, boundary conditions, and integral constraints. Here p denotes one or more parameters. AUTO can also do certain continuation and evolution computations for parabolic PDEs. It also includes the software HOMCONT for the bifurcation analysis of homoclinic orbits. AUTO is quite fast and can benefit from multiple processors; therefore it is applicable to rather large systems of differential equations.

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  1. Lavalle, Gianluca; Li, Yiqin; Mergui, Sophie; Grenier, Nicolas; Dietze, Georg F.: Suppression of the Kapitza instability in confined falling liquid films (2019)
  2. Alfaro, Matthieu; Izuhara, Hirofumi; Mimura, Masayasu: On a nonlocal system for vegetation in drylands (2018)
  3. Alnahdi, A. S.; Niesen, J.; Rucklidge, A. M.: Localized patterns in periodically forced systems. II: Patterns with nonzero wavenumber (2018)
  4. Amabili, Marco: Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory (2018)
  5. Barker, B.; Humpherys, J.; Lyng, G.; Lytle, J.: Evans function computation for the stability of travelling waves (2018)
  6. Bilinsky, L. M.; Baer, S. M.: Slow passage through a Hopf bifurcation in excitable nerve cables: spatial delays and spatial memory effects (2018)
  7. Brubaker, Nicholas D.: A continuation method for computing constant mean curvature surfaces with boundary (2018)
  8. 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)
  9. Charpentier, Isabelle; Cochelin, Bruno: Towards a full higher order AD-based continuation and bifurcation framework (2018)
  10. Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter: Sequential noise-induced escapes for oscillatory network dynamics (2018)
  11. Depetri, Gabriela I.; Pereira, Felipe A. C.; Marin, Boris; Baptista, Murilo S.; Sartorelli, J. C.: Dynamics of a parametrically excited simple pendulum (2018)
  12. Desroches, Mathieu; Kirk, Vivien: Spike-adding in a canonical three-time-scale model: superslow explosion and folded-saddle canards (2018)
  13. Farjami, Saeed; Kirk, Vivien; Osinga, Hinke M.: Computing the stable manifold of a saddle slow manifold (2018)
  14. Ferrario, Andrea; Merrison-Hort, Robert; Soffe, Stephen R.; Li, Wen-Chang; Borisyuk, Roman: Bifurcations of limit cycles in a reduced model of the Xenopus tadpole central pattern generator (2018)
  15. Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M.: Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study (2018)
  16. Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M.: Saddle slow manifolds and canard orbits in $\mathbbR^4$ and application to the full Hodgkin-Huxley model (2018)
  17. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Fold-pitchfork bifurcation, Arnold tongues and multiple chaotic attractors in a minimal network of three sigmoidal neurons (2018)
  18. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  19. Ibrahim, Bashar: Mathematical modeling and numerical simulation of the mitotic spindle orientation system (2018)
  20. Izuhara, Hirofumi; Kuto, Kousuke; Tsujikawa, Tohru: Bifurcation structure of stationary solutions for a chemotaxis system with bistable growth (2018)

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