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. Wei, Junqiang: Numerical optimization method for determination of bifurcation points and its application in stability analysis of power system (2020)
  2. Yang, Caroline; Rodriguez, Nancy: A numerical perspective on traveling wave solutions in a system for rioting activity (2020)
  3. Aldebert, Clement; Kooi, Bob W.; Nerini, David; Gauduchon, Mathias; Poggiale, Jean-Christophe: Three-dimensional bifurcation analysis of a predator-prey model with uncertain formulation (2019)
  4. Almet, Axel A.; Byrne, Helen M.; Maini, Philip K.; Moulton, Derek E.: Post-buckling behaviour of a growing elastic rod (2019)
  5. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts (2019)
  6. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Large scale patterns in mussel beds: stripes or spots? (2019)
  7. Hajnová, Veronika; Přibylová, Lenka: Bifurcation manifolds in predator-prey models computed by Gröbner basis method (2019)
  8. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Quasiperiodicity and chaos through Hopf-Hopf bifurcation in minimal ring neural oscillators due to a single shortcut (2019)
  9. Iuorio, Annalisa; Popović, Nikola; Szmolyan, Peter: Singular perturbation analysis of a regularized MEMS model (2019)
  10. Jenner, Adrianne L.; Kim, Peter S.; Frascoli, Federico: Oncolytic virotherapy for tumours following a Gompertz growth law (2019)
  11. Kaufman, Marcelle; Soulé, Christophe: On the multistationarity of chemical reaction networks (2019)
  12. Köksal Ersöz, Elif; Desroches, Mathieu; Mirasso, Claudio R.; Rodrigues, Serafim: Anticipation via canards in excitable systems (2019)
  13. Lavalle, Gianluca; Li, Yiqin; Mergui, Sophie; Grenier, Nicolas; Dietze, Georg F.: Suppression of the Kapitza instability in confined falling liquid films (2019)
  14. Lee, Min-Gi; Katsaounis, Theodoros; Tzavaras, Athanasios E.: Localization in adiabatic shear flow via geometric theory of singular perturbations (2019)
  15. Martínez-Jeraldo, Nicole; Aguirre, Pablo: Allee effect acting on the prey species in a Leslie-Gower predation model (2019)
  16. McLachlan, Robert I.; Offen, Christian: Symplectic integration of boundary value problems (2019)
  17. Morita, Hidetoshi; Inatsu, Masaru; Kokubu, Hiroshi: Topological computation analysis of meteorological time-series data (2019)
  18. Postlethwaite, Claire M.; Rucklidge, Alastair M.: A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock-Paper-Scissors (2019)
  19. Roussel, Marc R.: Nonlinear dynamics. A hands-on introductory survey (2019)
  20. Thompson, Alice B.; Gomes, Susana N.; Denner, Fabian; Dallaston, Michael C.; Kalliadasis, Serafim: Robust low-dimensional modelling of falling liquid films subject to variable wall heating (2019)

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