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.

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  1. Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter: Sequential noise-induced escapes for oscillatory network dynamics (2018)
  2. Desroches, Mathieu; Kirk, Vivien: Spike-adding in a canonical three-time-scale model: superslow explosion and folded-saddle canards (2018)
  3. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Fold-pitchfork bifurcation, Arnold tongues and multiple chaotic attractors in a minimal network of three sigmoidal neurons (2018)
  4. Simons, Julie; Fauci, Lisa: A model for the acrosome reaction in mammalian sperm (2018)
  5. Solis, Francisco J.; Saldaña, Fernando: Biological mechanisms of coexistence for a family of age structured population models (2018)
  6. Chapman, S. J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  7. Leonov, G. A.; Andrievskiy, B. R.; Mokaev, R. N.: Asymptotic behavior of solutions of Lorenz-like systems: analytical results and computer error structures (2017)
  8. Chang, Yu; Wang, Xiaoli; Xu, Dashun: Bifurcation analysis of a power system model with three machines and four buses (2016)
  9. Gani, M. Osman; Ogawa, Toshiyuki: Instability of periodic traveling wave solutions in a modified Fitzhugh-Nagumo model for excitable media (2015)
  10. Guckenheimer, John; Lizarraga, Ian: Shilnikov homoclinic bifurcation of mixed-mode oscillations (2015)
  11. Net, M.; Sánchez, J.: Continuation of bifurcations of periodic orbits for large-scale systems (2015)
  12. Nicola, Wilten; Ly, Cheng; Campbell, Sue Ann: One-dimensional population density approaches to recurrently coupled networks of neurons with noise (2015)
  13. Starostin, E. L.; van der Heijden, G. H. M.: Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips (2015)
  14. Boiko, Igor: Finding exact periodic solutions in Lur’e systems through periodic signal mapping (2014)
  15. Horikawa, Yo: Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons (2014)
  16. Kuznetsov, Yu. A.; Meijer, H. G. E.; Al Hdaibat, B.; Govaerts, W.: Improved homoclinic predictor for Bogdanov-Takens bifurcation (2014)
  17. Solis, Francisco J.; Ku-Carrillo, Roberto A.: Generic predation in age structure predator-prey models (2014)
  18. Asif, Mohammad; Ali, Emad; Ajbar, Abdelhamid: On the existence of chaotic behaviour in pure and simple microbial competition: the role of Contois kinetics (2013)
  19. Horikawa, Yo: Metastable and chaotic transient rotating waves in a ring of unidirectionally coupled bistable Lorenz systems (2013)
  20. Sherratt, Jonathan A.: Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations (2013)

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