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. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  2. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
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  4. Flynn, Andrew; Tsachouridis, Vassilios A.; Amann, Andreas: Multifunctionality in a reservoir computer (2021)
  5. Izuhara, Hirofumi; Kobayashi, Shunsuke: Spatio-temporal coexistence in the cross-diffusion competition system (2021)
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  7. Levasseur, Tyler; Palacios, Antonio: Asymptotic analysis of bifurcations in feedforward networks (2021)
  8. Liu, Yue; Rens, Elisabeth G.; Edelstein-Keshet, Leah: Spots, stripes, and spiral waves in models for static and motile cells. GTPase patterns in cells (2021)
  9. Pusuluri, Krishna; Meijer, H. G. E.; Shilnikov, A. L.: (INVITED) Homoclinic puzzles and chaos in a nonlinear laser model (2021)
  10. Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J.: High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities (2021)
  11. Sánchez Umbría, J.; Net, M.: Continuation of double Hopf points in thermal convection of rotating fluid spheres (2021)
  12. Sander, Evelyn; Wanner, Thomas: Equilibrium validation in models for pattern formation based on Sobolev embeddings (2021)
  13. Serrano, Sergio; Martínez, M. Angeles; Barrio, Roberto: Order in chaos: structure of chaotic invariant sets of square-wave neuron models (2021)
  14. van den Berg, Jan Bouwe; Queirolo, Elena: A general framework for validated continuation of periodic orbits in systems of polynomial ODEs (2021)
  15. Wang, Li; Lu, Zhong-Rong; Liu, Jike: Convergence rates of harmonic balance method for periodic solution of smooth and non-smooth systems (2021)
  16. Yagasaki, Kazuyuki; Yamazoe, Shotaro: Numerical analyses for spectral stability of solitary waves near bifurcation points (2021)
  17. Acampora, Luigi; Marra, Francesco S.: Numerical algorithms for the parametric continuation of stiff ODEs deriving from the modeling of combustion with detailed chemical mechanisms (2020)
  18. Andò, Alessia; Breda, Dimitri; Scarabel, Francesca: Numerical continuation and delay equations: a novel approach for complex models of structured populations (2020)
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  20. Barker, Blake; James, Jason Mireles; Morgan, Jalen: Parameterization method for unstable manifolds of standing waves on the line (2020)

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