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. Baspinar, E.; Avitabile, D.; Desroches, M.: Canonical models for torus canards in elliptic bursters (2021)
  2. Bengochea, Abimael; Galán-Vioque, Jorge; Pérez-Chavela, Ernesto: Families of symmetric exchange orbits in the planar ((1+2n))-body problem (2021)
  3. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  4. Cass, J. F.; Hogan, S. J.: Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination (2021)
  5. Cilenti, Lautaro; Balachandran, Balakumar: Transient probability in basins of noise influenced responses of mono and coupled Duffing oscillators (2021)
  6. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
  7. Coria, Lourdes; Lopez, Horacio; Palacios, Antonio; In, Visarath; Longhini, Patrick: Phase drift in networks of coupled colpitts oscillators (2021)
  8. Flynn, Andrew; Tsachouridis, Vassilios A.; Amann, Andreas: Multifunctionality in a reservoir computer (2021)
  9. Hasan, Cris R.; Osinga, Hinke M.; Postlethwaite, Claire M.; Rucklidge, Alastair M.: Spatiotemporal stability of periodic travelling waves in a heteroclinic-cycle model (2021)
  10. Izuhara, Hirofumi; Kobayashi, Shunsuke: Spatio-temporal coexistence in the cross-diffusion competition system (2021)
  11. Kecik, Krzysztof: Simultaneous vibration mitigation and energy harvesting from a pendulum-type absorber (2021)
  12. Levasseur, Tyler; Palacios, Antonio: Asymptotic analysis of bifurcations in feedforward networks (2021)
  13. 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)
  14. Mulugeta, Biruk Tafesse; Yu, Liping; Ren, Jingli: Bifurcation analysis of a one-prey and two-predators model with additional food and harvesting subject to toxicity (2021)
  15. Pototsky, Andrey; Oron, Alexander; Bestehorn, Michael: Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid (2021)
  16. Pusuluri, Krishna; Meijer, H. G. E.; Shilnikov, A. L.: (INVITED) Homoclinic puzzles and chaos in a nonlinear laser model (2021)
  17. 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)
  18. Saito, Takeshi; Yagasaki, Kazuyuki: Chebyshev spectral methods for computing center manifolds (2021)
  19. Sánchez Umbría, J.; Net, M.: Continuation of double Hopf points in thermal convection of rotating fluid spheres (2021)
  20. Sander, Evelyn; Wanner, Thomas: Equilibrium validation in models for pattern formation based on Sobolev embeddings (2021)

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