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. Contento, Lorenzo; Mimura, Masayasu: Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system (2020)
  2. Francke, M.; Pogromsky, A.; Nijmeijer, H.: Huygens’ clocks: `sympathy’ and resonance (2020)
  3. Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.: Analytical approximation of cuspidal loops using a nonlinear time transformation method (2020)
  4. Rand, Richard H.; Zehnder, Alan T.; Shayak, B.; Bhaskar, Aditya: Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators (2020)
  5. Rega, Giuseppe: Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh’s legacy (2020)
  6. Wei, Junqiang: Numerical optimization method for determination of bifurcation points and its application in stability analysis of power system (2020)
  7. Xu, Yifang; Krause, Andrew L.; Van Gorder, Robert A.: Generalist predator dynamics under Kolmogorov versus non-Kolmogorov models (2020)
  8. Yagasaki, Kazuyuki; Stachowiak, Tomasz: Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in (\mathbbR^d) for (d=3,4) (2020)
  9. Yang, Caroline; Rodriguez, Nancy: A numerical perspective on traveling wave solutions in a system for rioting activity (2020)
  10. Alcorta, Roberto; Baguet, Sebastien; Prabel, Benoit; Piteau, Philippe; Jacquet-Richardet, Georges: Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances (2019)
  11. Aldebert, Clement; Kooi, Bob W.; Nerini, David; Gauduchon, Mathias; Poggiale, Jean-Christophe: Three-dimensional bifurcation analysis of a predator-prey model with uncertain formulation (2019)
  12. Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J.: A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form (2019)
  13. Almet, Axel A.; Byrne, Helen M.; Maini, Philip K.; Moulton, Derek E.: Post-buckling behaviour of a growing elastic rod (2019)
  14. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts (2019)
  15. Bennett, Jamie J. R.; Sherratt, Jonathan A.: Large scale patterns in mussel beds: stripes or spots? (2019)
  16. Elliott, A. J.; Cammarano, A.; Neild, S. A.; Hill, T. L.; Wagg, D. J.: Using frequency detuning to compare analytical approximations for forced responses (2019)
  17. Guillot, Louis; Cochelin, Bruno; Vergez, Christophe: A Taylor series-based continuation method for solutions of dynamical systems (2019)
  18. Hajnová, Veronika; Přibylová, Lenka: Bifurcation manifolds in predator-prey models computed by Gröbner basis method (2019)
  19. Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna: Quasiperiodicity and chaos through Hopf-Hopf bifurcation in minimal ring neural oscillators due to a single shortcut (2019)
  20. Iuorio, Annalisa; Popović, Nikola; Szmolyan, Peter: Singular perturbation analysis of a regularized MEMS model (2019)

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