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. Kecik, Krzysztof: Simultaneous vibration mitigation and energy harvesting from a pendulum-type absorber (2021)
  2. Pusuluri, Krishna; Meijer, H. G. E.; Shilnikov, A. L.: (INVITED) Homoclinic puzzles and chaos in a nonlinear laser model (2021)
  3. 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)
  4. Andò, Alessia; Breda, Dimitri; Scarabel, Francesca: Numerical continuation and delay equations: a novel approach for complex models of structured populations (2020)
  5. Barrio, R.; Lozano, Á.; Rodríguez, M.; Serrano, S.: Numerical detection of patterns in CPGs: gait patterns in insect movement (2020)
  6. Bezekci, Burhan; Biktashev, V. N.: Strength-duration relationship in an excitable medium (2020)
  7. Bolzoni, Luca; Marca, Rossella Della; Groppi, Maria; Gragnani, Alessandra: Dynamics of a metapopulation epidemic model with localized culling (2020)
  8. Boscaggin, Alberto; Colasuonno, Francesca; Noris, Benedetta: Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions (2020)
  9. 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)
  10. Chang, Yu; Wang, Xiaoli; Feng, Zhihong; Feng, Wei: Bifurcation analysis in a cancer growth model (2020)
  11. Charalampidis, E. G.; Boullé, Nicolas; Farrell, Patrick E.; Kevrekidis, P. G.: Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation (2020)
  12. Cirillo, Giuseppe Ilario; Sepulchre, Rodolphe: The geometry of rest-spike bistability (2020)
  13. Cisternas, Jaime; Rohe, Kevin; Wehner, Stefan: Reaction-diffusion fronts and the butterfly set (2020)
  14. Contento, Lorenzo; Mimura, Masayasu: Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system (2020)
  15. Contreras-Julio, Dana; Aguirre, Pablo; Mujica, José; Vasilieva, Olga: Finding strategies to regulate propagation and containment of dengue via invariant manifold analysis (2020)
  16. Darki, Farzaneh; Rankin, James: Methods to assess binocular rivalry with periodic stimuli (2020)
  17. Farjami, Saeed; Alexander, Ryan P. D.; Bowie, Derek; Khadra, Anmar: Switching in cerebellar stellate cell excitability in response to a pair of inhibitory/excitatory presynaptic inputs: a dynamical system perspective (2020)
  18. 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)
  19. Francke, M.; Pogromsky, A.; Nijmeijer, H.: Huygens’ clocks: `sympathy’ and resonance (2020)
  20. Franović, Igor; Yanchuk, Serhiy; Eydam, Sebastian; Bačić, Iva; Wolfrum, Matthias: Dynamics of a stochastic excitable system with slowly adapting feedback (2020)

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