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. Blömker, Dirk; Sander, Evelyn; Wanner, Thomas: Degenerate nucleation in the Cahn-Hilliard-Cook model (2016)
  2. Boie, Sebastian; Kirk, Vivien; Sneyd, James; Wechselberger, Martin: Effects of quasi-steady-state reduction on biophysical models with oscillations (2016)
  3. Bonheure, Denis; Földes, Juraj; Saldaña, Alberto: Qualitative properties of solutions to mixed-diffusion bistable equations (2016)
  4. Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.: Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis (2016)
  5. Burke, John; Desroches, Mathieu; Granados, Albert; Kaper, Tasso J.; Krupa, Martin; Vo, Theodore: From canards of folded singularities to torus canards in a forced van der Pol equation (2016)
  6. Dawes, J.H.P.; Williams, J.L.M.: Localised pattern formation in a model for dryland vegetation (2016)
  7. Dercole, Fabio; Geritz, Stefan A.H.: Unfolding the resident-invader dynamics of similar strategies (2016)
  8. Kooi, Bob W.; Venturino, Ezio: Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey (2016)
  9. Sander, Evelyn; Wanner, Thomas: Validated saddle-node bifurcations and applications to lattice dynamical systems (2016)
  10. Sarode, Ketan Dinkar; Ravi Kumar, V.; Kulkarni, B.D.: Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm (2016)
  11. Trinh, Philippe H.; Ward, Michael J.: The dynamics of localized spot patterns for reaction-diffusion systems on the sphere (2016)
  12. Aguirre, Pablo: Bifurcations of two-dimensional global invariant manifolds near a noncentral saddle-node homoclinic orbit (2015)
  13. Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A.J.: Analysis of the T-point-Hopf bifurcation in the Lorenz system (2015)
  14. Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J.: Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems (2015)
  15. Audoly, Basile; Seffen, Keith A.: Buckling of naturally curved elastic strips: the ribbon model makes a difference (2015)
  16. Bakri, Taoufik; Kuznetsov, Yuri A.; Verhulst, Ferdinand: Torus bifurcations in a mechanical system (2015)
  17. Chalmers, Alexander D.; Cohen, Anna; Bursill, Christina A.; Myerscough, Mary R.: Bifurcation and dynamics in a mathematical model of early atherosclerosis, How acute inflammation drives lesion development (2015)
  18. Contento, Lorenzo; Mimura, Masayasu; Tohma, Makoto: Two-dimensional traveling waves arising from planar front interaction in a three-species competition-diffusion system (2015)
  19. Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M.: Global organization of phase space in the transition to chaos in the Lorenz system (2015)
  20. Erdoğan, M.B.; Marzuola, J.L.; Newhall, K.; Tzirakis, N.: The structure of global attractors for dissipative Zakharov systems with forcing on the torus (2015)

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