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.

References in zbMATH (referenced in 38 articles )

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  1. Mitry, John; Wechselberger, Martin: Folded saddles and faux canards (2017)
  2. Kristiansen, K.Uldall: Computation of saddle-type slow manifolds using iterative methods (2015)
  3. Sahoo, Banshidhar; Poria, Swarup: Chaos to order: role of additional food to predator in a food chain model (2015)
  4. Ducceschi, Michele; Touzé, Cyril; Bilbao, Stefan; Webb, Craig J.: Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations (2014)
  5. Ei, Shin-Ichiro; Izuhara, Hirofumi; Mimura, Masayasu: Spatio-temporal oscillations in the Keller-Segel system with logistic growth (2014)
  6. Roberts, A.J.; MacKenzie, T.; Bunder, J.E.: A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions (2014)
  7. Wagener, Florian: Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict (2013)
  8. Sun, Gui-Quan; Zhang, Juan; Song, Li-Peng; Jin, Zhen; Li, Bai-Lian: Pattern formation of a spatial predator-prey system (2012)
  9. Wang, Yunjiao; Paszek, Pawel; Horton, Caroline A.; Yue, Hong; White, Michael R.H.; Kell, Douglas B.; Muldoon, Mark R.; Broomhead, David S.: A systematic survey of the response of a model NF-$\kappa$B signalling pathway to $\mathrmTNF\alpha$ stimulation (2012)
  10. Barrio, R.; Blesa, F.; Dena, A.; Serrano, S.: Qualitative and numerical analysis of the Rössler model: bifurcations of equilibria (2011)
  11. Kumar, Ajeet; Hui, Chung-Yuen: Numerical study of shearing of a microfibre during friction testing of a microfibre array (2011)
  12. Amdjadi, Faridon: A numerical method for the dynamics and stability of spiral waves (2010)
  13. Bordyugov, Grigory; Fischer, Nils; Engel, Harald; Manz, Niklas; Steinbock, Oliver: Anomalous dispersion in the Belousov-Zhabotinsky reaction: experiments and modeling (2010)
  14. Kumar, Ajeet; Healey, Timothy J.: A generalized computational approach to stability of static equilibria of nonlinearly elastic rods in the presence of constraints (2010)
  15. Barrio, Roberto; Blesa, Fernando: Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems (2009)
  16. Kehrt, M.; Hövel, P.; Flunkert, V.; Dahlem, M.A.; Rodin, P.; Schöll, E.: Stabilization of complex spatio-temporal dynamics near a subcritical Hopf bifurcation by time-delayed feedback (2009)
  17. Nandakumar, K.; Chatterjee, Anindya: Continuation of limit cycles near saddle homoclinic points using splines in phase space (2009)
  18. Pokorny, P.: Continuation of periodic solutions of dissipative and conservative systems: application to elastic pendulum (2009)
  19. Valverde, J.; García-Vallejo, D.: Stability analysis of a substructured model of the rotating beam (2009)
  20. Wechselberger, Martin; Weckesser, Warren: Bifurcations of mixed-mode oscillations in a stellate cell model (2009)

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