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. Al Saadi, Fahad; Worthy, Annette; Alrihieli, Haifaa; Nelson, Mark: Localised spatial structures in the Thomas model (2022)
  2. Engel, Maximilian; Kuehn, Christian; Petrera, Matteo; Suris, Yuri: Discretized fast-slow systems with canards in two dimensions (2022)
  3. Goh, Ryan; de Rijk, Björn: Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism (2022)
  4. Kabir, M. Humayun; Gani, M. Osman: Numerical bifurcation analysis and pattern formation in a minimal reaction-diffusion model for vegetation (2022)
  5. Kuwamura, Masataka; Izuhara, Hirofumi; Ei, Shin-ichiro: Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation (2022)
  6. Uecker, Hannes: Continuation and bifurcation in nonlinear PDEs - algorithms, applications, and experiments (2022)
  7. Yagasaki, Kazuyuki; Yamazoe, Shotaro: Numerical computations for bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations (2022)
  8. Al-Salman, Ahd Mahmoud; Páez Chávez, Joseph; Wijaya, Karunia Putra: A modeling study of predator-prey interaction propounding honest signals and cues (2021)
  9. Amuzescu, Bogdan; Airini, Razvan; Epureanu, Florin Bogdan; Mann, Stefan A.; Knott, Thomas; Radu, Beatrice Mihaela: Evolution of mathematical models of cardiomyocyte electrophysiology (2021)
  10. Arancibia-Ibarra, Claudio; Aguirre, Pablo; Flores, José; van Heijster, Peter: Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response (2021)
  11. Ashwin, Peter; Postlethwaite, Claire: Excitable networks for finite state computation with continuous time recurrent neural networks (2021)
  12. Baspinar, E.; Avitabile, D.; Desroches, M.: Canonical models for torus canards in elliptic bursters (2021)
  13. Bengochea, Abimael; Galán-Vioque, Jorge; Pérez-Chavela, Ernesto: Families of symmetric exchange orbits in the planar ((1+2n))-body problem (2021)
  14. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  15. Cass, J. F.; Hogan, S. J.: Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination (2021)
  16. Champneys, Alan R.; Al Saadi, Fahad; Breña-Medina, Victor F.; Grieneisen, Verônica A.; Marée, Athanasius F. M.; Verschueren, Nicolas; Wuyts, Bert: Bistability, wave pinning and localisation in natural reaction-diffusion systems (2021)
  17. Cilenti, Lautaro; Balachandran, Balakumar: Transient probability in basins of noise influenced responses of mono and coupled Duffing oscillators (2021)
  18. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
  19. Coria, Lourdes; Lopez, Horacio; Palacios, Antonio; In, Visarath; Longhini, Patrick: Phase drift in networks of coupled colpitts oscillators (2021)
  20. Fabiani, Gianluca; Calabrò, Francesco; Russo, Lucia; Siettos, Constantinos: Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines (2021)

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