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.

References in zbMATH (referenced in 681 articles , 1 standard article )

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  1. Alnahdi, A. S.; Niesen, J.; Rucklidge, A. M.: Localized patterns in periodically forced systems. II. Patterns with nonzero wavenumber (2018)
  2. Bilinsky, L. M.; Baer, S. M.: Slow passage through a Hopf bifurcation in excitable nerve cables: spatial delays and spatial memory effects (2018)
  3. Brubaker, Nicholas D.: A continuation method for computing constant mean curvature surfaces with boundary (2018)
  4. Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter: Sequential noise-induced escapes for oscillatory network dynamics (2018)
  5. Depetri, Gabriela I.; Pereira, Felipe A. C.; Marin, Boris; Baptista, Murilo S.; Sartorelli, J. C.: Dynamics of a parametrically excited simple pendulum (2018)
  6. Farjami, Saeed; Kirk, Vivien; Osinga, Hinke M.: Computing the stable manifold of a saddle slow manifold (2018)
  7. 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)
  8. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  9. Kooi, B. W.; Poggiale, J. C.: Modelling, singular perturbation and bifurcation analyses of bitrophic food chains (2018)
  10. Li, Mingwu; Dankowicz, Harry: Staged construction of adjoints for constrained optimization of integro-differential boundary-value problems (2018)
  11. Liu, Yan; You, Zai-Jin; Gao, Shi-Zhao: A continuous 1-D model for the coiling of a weakly viscoelastic jet (2018)
  12. Miyaji, Tomoyuki; Tsutsumi, Yoshio: Steady-state mode interactions of radially symmetric modes for the Lugiato-Lefever equation on a disk (2018)
  13. Mujica, José; Krauskopf, Bernd; Osinga, Hinke M.: Tangencies between global invariant manifolds and slow manifolds near a singular Hopf bifurcation (2018)
  14. Novbari, E.; Oron, A.: Parametric excitation of an axisymmetric flow of a thin liquid film down a vertical fiber (2018)
  15. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  16. Solis, Francisco J.; Saldaña, Fernando: Biological mechanisms of coexistence for a family of age structured population models (2018)
  17. Yagasaki, Kazuyuki: Melnikov processes and chaos in randomly perturbed dynamical systems (2018)
  18. Banerjee, M.; Kooi, Bob W.; Venturino, E.: An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey (2017)
  19. Baresi, Nicola; Scheeres, Daniel J.: Bounded relative motion under zonal harmonics perturbations (2017)
  20. Bonheure, Denis; Casteras, Jean-Baptiste; Noris, Benedetta: Multiple positive solutions of the stationary Keller-Segel system (2017)

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