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 802 articles , 1 standard article )

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  1. Wang, Hua O.; Abed, Eyad H.: Bifurcation control of a chaotic system (1995)
  2. Alhumaizi, Khalid; Aris, Rutherford: Chaos in a simple two-phase reactor (1994)
  3. Aronson, D. G.; van Gils, S. A.; Krupa, M.: Homoclinic twist bifurcations with (\mathbbZ_ 2) symmetry (1994)
  4. Bai, Fengshan; Spence, Alastair; Stuart, Andrew M.: Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation (1994)
  5. Balakrishnan, E.; Swift, A.; Wake, G. C.: Path-following for disjoint bifurcation problems arising in ignition theory (1994)
  6. Bertram, Richard: Reduced-system analysis of the effects of serotonin on a molluscan burster neuron (1994)
  7. Champneys, A. R.; Kuznetsov, Yu. A.: Numerical detection and continuation of codimension-two homoclinic bifurcations (1994)
  8. Chen, Guanrong: An overview of bifurcation, chaos and nonlinear dynamics in control systems (1994)
  9. Chiang, Hsiao-Dong; Conneen, Timothy P.; Flueck, Alexander J.: Bifurcations and chaos in electric power systems: Numerical studies (1994)
  10. Dillon, R.; Maini, P. K.; Othmer, Hans G.: Pattern formation in generalized Turing systems. I: Steady-state patterns in systems with mixed boundary conditions (1994)
  11. Doedel, Eusebius J.; Friedman, Mark J.; Monteiro, Anand C.: On locating connecting orbits (1994)
  12. Golden Kusch, Melinda; Ydstie, B. Erik: Drift instabilities and chaos in forecasting and adaptive decision theory (1994)
  13. Krauskopf, Bernd: The bifurcation set for the (1:4) resonance problem (1994)
  14. Lenas, Petros; Pavlou, Stavros: Periodic, quasi-periodic, and chaotic coexistence of two competing microbial populations in a periodically operated chemostat (1994)
  15. Price, C. B.: Turing hexagons in pure cubic nonlinear fields (1994)
  16. Reyna, Luis G.; Ward, Michael J.: Resolving weak internal layer interactions for the Ginzburg-Landau equation (1994)
  17. Rumpf, B.; Sauermann, H.: Bifurcations of two coupled classical spin oscillators (1994)
  18. Rush, Maureen E.; Rinzel, John: Analysis of bursting in a thalamic neuron model (1994)
  19. Scotter, Miguel; Swift, Adrian: Path-following, critical points and shape factors (1994)
  20. Taylor, Mark A.; Pavlou, Stavros; Kevrekidis, Ioannis G.: Microbial predation in coupled chemostats: A global study of two coupled nonlinear oscillators (1994)

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