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. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  2. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  3. Baresi, Nicola; Scheeres, Daniel J.: Bounded relative motion under zonal harmonics perturbations (2017)
  4. Bonheure, Denis; Casteras, Jean-Baptiste; Noris, Benedetta: Multiple positive solutions of the stationary Keller-Segel system (2017)
  5. Chapman, S.J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  6. Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M.: Finding first foliation tangencies in the Lorenz system (2017)
  7. 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)
  8. 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)
  9. Engler, Hans; Kaper, Hans G.; Kaper, Tasso J.; Vo, Theodore: Dynamical systems analysis of the Maasch-Saltzman model for glacial cycles (2017)
  10. 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)
  11. Grass, Dieter; Uecker, Hannes: Optimal management and spatial patterns in a distributed shallow lake model (2017)
  12. Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M.: Mixed-mode oscillations and twin canard orbits in an autocatalytic chemical reaction (2017)
  13. Ibrahim, Bashar: A mathematical framework for kinetochore-driven activation feedback in the mitotic checkpoint (2017)
  14. Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier: A numerical study of nonlinear dispersive wave models with $\mathsfSpecTraVVave$ (2017)
  15. Köksal Ersöz, Elif; Desroches, Mathieu; Krupa, Martin: Synchronization of weakly coupled canard oscillators (2017)
  16. Langfield, Peter; Façanha, Wilson L.C.; Oldeman, Bart; Glass, Leon: Bifurcations in a periodically stimulated limit cycle oscillator with finite relaxation times (2017)
  17. Leonov, G.A.; Andrievskiy, B.R.; Mokaev, R.N.: Asymptotic behavior of solutions of Lorenz-like systems: analytical results and computer error structures (2017)
  18. 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)
  19. Mandel, Rainer; Reichel, Wolfgang: A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation (2017)
  20. Mitry, John; Wechselberger, Martin: Folded saddles and faux canards (2017)

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