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. Horikawa, Yo: Bifurcations and chaos in a minimal neural network: forced coupled neurons (2021)
  2. Sánchez Umbría, J.; Net, M.: Continuation of double Hopf points in thermal convection of rotating fluid spheres (2021)
  3. Bezekci, Burhan; Biktashev, V. N.: Strength-duration relationship in an excitable medium (2020)
  4. Chang, Yu; Wang, Xiaoli; Feng, Zhihong; Feng, Wei: Bifurcation analysis in a cancer growth model (2020)
  5. Charalampidis, E. G.; Boullé, Nicolas; Farrell, Patrick E.; Kevrekidis, P. G.: Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation (2020)
  6. Hajnová, Veronika; Přibylová, Lenka: Bifurcation manifolds in predator-prey models computed by Gröbner basis method (2019)
  7. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Quasiperiodicity and chaos through Hopf-Hopf bifurcation in minimal ring neural oscillators due to a single shortcut (2019)
  8. Lee, Min-Gi; Katsaounis, Theodoros; Tzavaras, Athanasios E.: Localization in adiabatic shear flow via geometric theory of singular perturbations (2019)
  9. Morita, Hidetoshi; Inatsu, Masaru; Kokubu, Hiroshi: Topological computation analysis of meteorological time-series data (2019)
  10. Thompson, J. Michael T.; Virgin, Lawrence N.: Instabilities of nonconservative fluid-loaded systems (2019)
  11. Walawska, Irmina; Wilczak, Daniel: Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems (2019)
  12. Creaser, Jennifer; Tsaneva-Atanasova, Krasimira; Ashwin, Peter: Sequential noise-induced escapes for oscillatory network dynamics (2018)
  13. Desroches, Mathieu; Kirk, Vivien: Spike-adding in a canonical three-time-scale model: superslow explosion and folded-saddle canards (2018)
  14. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Fold-pitchfork bifurcation, Arnold tongues and multiple chaotic attractors in a minimal network of three sigmoidal neurons (2018)
  15. Kelley, C. T.: Numerical methods for nonlinear equations (2018)
  16. Simons, Julie; Fauci, Lisa: A model for the acrosome reaction in mammalian sperm (2018)
  17. Solis, Francisco J.; Saldaña, Fernando: Biological mechanisms of coexistence for a family of age structured population models (2018)
  18. Chapman, S. J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  19. Leonov, G. A.; Andrievskiy, B. R.; Mokaev, R. N.: Asymptotic behavior of solutions of Lorenz-like systems: analytical results and computer error structures (2017)
  20. Chang, Yu; Wang, Xiaoli; Xu, Dashun: Bifurcation analysis of a power system model with three machines and four buses (2016)

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