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. Bolzoni, Luca; Marca, Rossella Della; Groppi, Maria; Gragnani, Alessandra: Dynamics of a metapopulation epidemic model with localized culling (2020)
  2. Boscaggin, Alberto; Colasuonno, Francesca; Noris, Benedetta: Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions (2020)
  3. Bruni, Stefano; Meijaard, J. P.; Rill, Georg; Schwab, A. L.: State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches (2020)
  4. Chang, Yu; Wang, Xiaoli; Feng, Zhihong; Feng, Wei: Bifurcation analysis in a cancer growth model (2020)
  5. Contento, Lorenzo; Mimura, Masayasu: Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system (2020)
  6. Contreras-Julio, Dana; Aguirre, Pablo; Mujica, José; Vasilieva, Olga: Finding strategies to regulate propagation and containment of dengue via invariant manifold analysis (2020)
  7. Fatoyinbo, H. O.; Brown, R. G.; Simpson, D. J. W.; van Brunt, B.: Numerical bifurcation analysis of pacemaker dynamics in a model of smooth muscle cells (2020)
  8. Francke, M.; Pogromsky, A.; Nijmeijer, H.: Huygens’ clocks: `sympathy’ and resonance (2020)
  9. Gerlach, Raphael; Ziessler, Adrian; Eckhardt, Bruno; Dellnitz, Michael: A set-oriented path following method for the approximation of parameter dependent attractors (2020)
  10. Guillot, Louis; Lazarus, Arnaud; Thomas, Olivier; Vergez, Christophe; Cochelin, Bruno: A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems (2020)
  11. Iuorio, Annalisa; Kuehn, Christian; Szmolyan, Peter: Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem (2020)
  12. Lestringant, Claire; Audoly, Basile; Kochmann, Dennis M.: A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams (2020)
  13. Letson, Benjamin; Rubin, Jonathan E.: LOR for analysis of periodic dynamics: a one-stop shop approach (2020)
  14. Lin, Wei; Páez Chávez, Joseph; Liu, Yang; Yang, Yingxin; Kuang, Yuchun: Stick-slip suppression and speed tuning for a drill-string system via proportional-derivative control (2020)
  15. Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.: Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field (2020)
  16. Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.: High-order analysis of canard explosion in the Brusselator equations (2020)
  17. Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.: Analytical approximation of cuspidal loops using a nonlinear time transformation method (2020)
  18. Rand, Richard H.; Zehnder, Alan T.; Shayak, B.; Bhaskar, Aditya: Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators (2020)
  19. Rega, Giuseppe: Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh’s legacy (2020)
  20. Rivera, Viviana; Aguirre, Pablo: Study of a tritrophic food chain model with non-differentiable functional response (2020)

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