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 formf(u,p) = 0, f,u in Rnand of systems of ordinary differential equations of the formu”(t) = f(u(t),p), f,u in Rnsubject 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 242 articles )

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  1. Chapman, S.J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  2. Gani, M.Osman; Ogawa, Toshiyuki: Instability of periodic traveling wave solutions in a modified Fitzhugh-Nagumo model for excitable media (2015)
  3. Nicola, Wilten; Ly, Cheng; Campbell, Sue Ann: One-dimensional population density approaches to recurrently coupled networks of neurons with noise (2015)
  4. Starostin, E.L.; van der Heijden, G.H.M.: Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips (2015)
  5. Horikawa, Yo: Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons (2014)
  6. Horikawa, Yo: Metastable and chaotic transient rotating waves in a ring of unidirectionally coupled bistable Lorenz systems (2013)
  7. Sherratt, Jonathan A.: Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations (2013)
  8. Braza, Peter A.: Predator-prey dynamics with square root functional responses (2012)
  9. Kanai, Y.; Yabuno, H.: Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator (2012)
  10. Ajbar, Abdelhamid; Alahmad, Malik; Ali, Emad: On the dynamics of biodegradation of wastewater in aerated continuous bioreactors (2011)
  11. Solis, Francisco J.; Ku, Roberto A.: Nonlinear juvenile predation population dynamics (2011)
  12. Theodosiou, C.; Pournaras, A.; Natsiavas, S.: On periodic steady state response and stability of Filippov-type mechanical models (2011)
  13. Wang, Wanyong; Xu, Jian: Multiple scales analysis for double Hopf bifurcation with 1:3 resonance (2011)
  14. Broeckhove, Jan; Kłosiewicz, Przemysław; Vanroose, Wim: Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation (2010)
  15. Dick, Andrew J.; Balachandran, Balakumar; Yabuno, Hiroshi; Numatsu, Masatoshi; Hayashi, Keiichi; Kuroda, Masaharu; Ashida, Kiwamu: Utilizing nonlinear phenomena to locate grazing in the constrained motion of a cantilever beam (2009)
  16. Theodosiou, C.; Sikelis, K.; Natsiavas, S.: Periodic steady state response of large scale mechanical models with local nonlinearities (2009)
  17. Kelley, C.T.; Liao, Li-Zhi; Qi, Liqun; Chu, Moody T.; Reese, J.P.; Winton, C.: Projected pseudotransient continuation (2008)
  18. Laing, Carlo R.; Kevrekidis, Ioannis G.: Periodically-forced finite networks of heterogeneous globally-coupled oscillators: a low-dimensional approach (2008)
  19. Modarres-Sadeghi, Yahya; Païdoussis, Michael P.; Semler, Christian: Three-dimensional oscillations of a cantilever pipe conveying fluid (2008)
  20. Seo, Gunog; Kot, Mark: A comparison of two predator-prey models with Holling’s type I functional response (2008)

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