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 568 articles , 1 standard article )

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  1. Baresi, Nicola; Scheeres, Daniel J.: Bounded relative motion under zonal harmonics perturbations (2017)
  2. Chapman, S.J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  3. 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)
  4. 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)
  5. Grass, Dieter; Uecker, Hannes: Optimal management and spatial patterns in a distributed shallow lake model (2017)
  6. Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier: A numerical study of nonlinear dispersive wave models with $\mathsfSpecTraVVave$ (2017)
  7. Langfield, Peter; Façanha, Wilson L.C.; Oldeman, Bart; Glass, Leon: Bifurcations in a periodically stimulated limit cycle oscillator with finite relaxation times (2017)
  8. 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)
  9. Mandel, Rainer; Reichel, Wolfgang: A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation (2017)
  10. Mitry, John; Wechselberger, Martin: Folded saddles and faux canards (2017)
  11. Stoykov, S.; Margenov, S.: Numerical methods and parallel algorithms for computation of periodic responses of plates (2017)
  12. Wanner, Thomas: Computer-assisted equilibrium validation for the diblock copolymer model (2017)
  13. Avitabile, Daniele; Słowiński, Piotr; Bardy, Benoit; Tsaneva-Atanasova, Krasimira: Beyond in-phase and anti-phase coordination in a model of joint action (2016)
  14. Blömker, Dirk; Sander, Evelyn; Wanner, Thomas: Degenerate nucleation in the Cahn-Hilliard-Cook model (2016)
  15. Boie, Sebastian; Kirk, Vivien; Sneyd, James; Wechselberger, Martin: Effects of quasi-steady-state reduction on biophysical models with oscillations (2016)
  16. Bonheure, Denis; Földes, Juraj; Saldaña, Alberto: Qualitative properties of solutions to mixed-diffusion bistable equations (2016)
  17. Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.: Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis (2016)
  18. Burke, John; Desroches, Mathieu; Granados, Albert; Kaper, Tasso J.; Krupa, Martin; Vo, Theodore: From canards of folded singularities to torus canards in a forced van der Pol equation (2016)
  19. Dawes, J.H.P.; Williams, J.L.M.: Localised pattern formation in a model for dryland vegetation (2016)
  20. Dercole, Fabio; Geritz, Stefan A.H.: Unfolding the resident-invader dynamics of similar strategies (2016)

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