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 672 articles , 1 standard article )

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  1. Bilinsky, L. M.; Baer, S. M.: Slow passage through a Hopf bifurcation in excitable nerve cables: spatial delays and spatial memory effects (2018)
  2. Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter: Sequential noise-induced escapes for oscillatory network dynamics (2018)
  3. Depetri, Gabriela I.; Pereira, Felipe A. C.; Marin, Boris; Baptista, Murilo S.; Sartorelli, J. C.: Dynamics of a parametrically excited simple pendulum (2018)
  4. Farjami, Saeed; Kirk, Vivien; Osinga, Hinke M.: Computing the stable manifold of a saddle slow manifold (2018)
  5. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  6. Kooi, B. W.; Poggiale, J. C.: Modelling, singular perturbation and bifurcation analyses of bitrophic food chains (2018)
  7. Liu, Yan; You, Zai-Jin; Gao, Shi-Zhao: A continuous 1-D model for the coiling of a weakly viscoelastic jet (2018)
  8. Novbari, E.; Oron, A.: Parametric excitation of an axisymmetric flow of a thin liquid film down a vertical fiber (2018)
  9. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  10. Solis, Francisco J.; Saldaña, Fernando: Biological mechanisms of coexistence for a family of age structured population models (2018)
  11. 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)
  12. Baresi, Nicola; Scheeres, Daniel J.: Bounded relative motion under zonal harmonics perturbations (2017)
  13. Bonheure, Denis; Casteras, Jean-Baptiste; Noris, Benedetta: Multiple positive solutions of the stationary Keller-Segel system (2017)
  14. Chapman, S. J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  15. Chehelcheraghi, Mojtaba; Nakatani, C.; van Leeuwen, C.: Analysis of an interneuron gamma mechanism for cross-frequency coupling (2017)
  16. Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M.: Finding first foliation tangencies in the Lorenz system (2017)
  17. Dallaston, M. C.; Tseluiko, D.; Zheng, Z.; Fontelos, M. A.; Kalliadasis, S.: Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows (2017)
  18. Dutta, Partha Sharathi; Kooi, Bob W.; Feudel, Ulrike: The impact of a predator on the outcome of competition in the three-trophic food web (2017)
  19. Engler, Hans; Kaper, Hans G.; Kaper, Tasso J.; Vo, Theodore: Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles (2017)
  20. 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)

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