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 740 articles , 1 standard article )

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  1. de Swart, H. E.: Analysis of a six-component atmospheric spectral model: Chaos, predictability and vacillation (1989)
  2. Doedel, Eusebius J; Friedman, Mark J.: Numerical computation of heteroclinic orbits (1989)
  3. de Swart, H. E.: Low-order spectral models of the atmospheric circulation: A survey (1988)
  4. DeYoung, G.; Monk, P. B.; Othmer, Hans G.: Pacemakers in aggregation fields of Dictyostelium discoideum: Does a single cell suffice? (1988)
  5. Dockery, J. D.; Keener, J. P.; Tyson, J. J.: Dispersion of traveling waves in the Belousov-Zhabotinskij reaction (1988)
  6. Kaas-Petersen, Christian; Scott, Stephen K.: Homoclinic orbits in a simple chemical model of an autocatalytic reaction (1988)
  7. Verlinden, P.; Cools, R.; Roose, D.; Haegemans, Ann: The construction of cubature formulae for a family of integrals: A bifurcation problem (1988)
  8. Wollkind, David J.; Collings, John B.; Logan, Jesse A.: Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit trees (1988)
  9. Aronson, D. G.; Doedel, E. J.; Othmer, H. G.: An analytical and numerical study of the bifurcations in a system of linearly-coupled oscillators (1987)
  10. Cronin, Jane: Mathematical aspects of Hodgkin-Huxley neural theory (1987)
  11. Georgopoulos, E.; Horwitz, J. A.; Rosenblat, S.: Double-diffusive convection in a circular cylinder (1987)
  12. Landau, Mayer; Lorente, Paco; Henry, Jacques; Canu, Stephane: Hysteresis phenomena between periodic and stationary solutions in a model of pacemaker and nonpacemaker coupled cardiac cells (1987)
  13. Poore, A. B.; Tiahrt, C. A.: Bifurcation problems in nonlinear parametric programming (1987)
  14. Rinzel, John; Seek, Young Lee: Dissection of a model for neuronal parabolic bursting (1987)
  15. Baer, Steven M.; Tier, Charles: An analysis of a dendritic neuron model with an active membrane site (1986)
  16. Griewank, A.; Reddien, G. W.: The approximation of generalized turning points by projection methods with superconvergence to the critical parameter (1986)
  17. Roose, D.: An algorithm for the computation of Hopf bifurcation points in comparison with other methods (1985)
  18. Doedel, Eusebius: The computer-aided bifurcation analysis of predator-prey models (1984)
  19. Doedel, Eusebius: AUTO: A program for the automatic bifurcation analysis of autonomous systems (1981)
  20. Hassard, B.; El-Henawy, I. M.: Numerical Hopf bifurcation analysis in nonlinear ordinary and partial differential systems from chemical reactor theory (1981)

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