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 52 articles )

Showing results 1 to 20 of 52.
Sorted by year (citations)

1 2 3 next

  1. Lu, Min; Huang, Jicai: Global analysis in Bazykin’s model with Holling II functional response and predator competition (2021)
  2. Kreusser, L. M.; McLachlan, R. I.; Offen, C.: Detection of high codimensional bifurcations in variational PDEs (2020)
  3. Witting, Katrin; Molo, Mirko Hessel-Von; Dellnitz, Michael: Structural properties of Pareto fronts: the occurrence of dents in classical and parametric multiobjective optimization problems (2020)
  4. Bick, Christian; Panaggio, Mark J.; Martens, Erik A.: Chaos in Kuramoto oscillator networks (2018)
  5. Tao, Molei: Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions (2018)
  6. Mitry, John; Wechselberger, Martin: Folded saddles and faux canards (2017)
  7. Renson, Ludovic; Barton, David A. W.; Neild, Simon A.: Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation (2017)
  8. Kristiansen, K. Uldall: Computation of saddle-type slow manifolds using iterative methods (2015)
  9. Sahoo, Banshidhar; Poria, Swarup: Chaos to order: role of additional food to predator in a food chain model (2015)
  10. Zgliczyński, Piotr: Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof (2015)
  11. Barrio, Roberto; Blesa, Fernando; Serrano, Sergio: Unbounded dynamics in dissipative flows: Rössler model (2014)
  12. Ducceschi, Michele; Touzé, Cyril; Bilbao, Stefan; Webb, Craig J.: Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations (2014)
  13. Ei, Shin-Ichiro; Izuhara, Hirofumi; Mimura, Masayasu: Spatio-temporal oscillations in the Keller-Segel system with logistic growth (2014)
  14. Roberts, A. J.; MacKenzie, T.; Bunder, J. E.: A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions (2014)
  15. Wagener, Florian: Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict (2013)
  16. Bribesh, Fathi A. M.; Fraštia, Ľubor; Thiele, Uwe: Decomposition driven interface evolution for layers of binary mixtures. III. Two-dimensional steady films with flat and modulated surfaces (2012)
  17. Sun, Gui-Quan; Zhang, Juan; Song, Li-Peng; Jin, Zhen; Li, Bai-Lian: Pattern formation of a spatial predator-prey system (2012)
  18. 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)
  19. Barrio, R.; Blesa, F.; Dena, A.; Serrano, S.: Qualitative and numerical analysis of the Rössler model: bifurcations of equilibria (2011)
  20. Kumar, Ajeet; Hui, Chung-Yuen: Numerical study of shearing of a microfibre during friction testing of a microfibre array (2011)

1 2 3 next