Publications
2021
Scholarly publications
Kuznetsov, Y. A., & Hooyman, J. (2021). Bifurcations of heteroclinic contours in two-parameter planar systems: Overview and explicit examples. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 31(12), [2130036]. https://doi.org/10.1142/S0218127421300366
Govaerts, W., Kuznetsov, Y. A., Meijer, H. G. E., Neirynck, N., & van Wezel, R. (2021). Bistability and Stabilization of Human Visual Perception under Ambiguous Stimulation. Nonlinear Dynamics, Psychology, and Life Sciences, 25(3), 297-307.
2020
Scholarly publications
Spek, L., Kuznetsov, Y. A., & van Gils, S. A. (2020). Neural field models with transmission delays and diffusion. The Journal of Mathematical Neuroscience, 10, 1-50. [21]. https://doi.org/10.1186/s13408-020-00098-5
Bosschaert, M. M., Janssens, S. G., & Kuznetsov, Y. A. (2020). Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations. SIAM Journal on Applied Dynamical Systems, 19(1), 252-303. https://doi.org/10.1137/19M1243993
2019
Scholarly publications
Kuznetsov, Y. A., & Meijer, H. G. E. (2019). Numerical Bifurcation Analysis of Maps: From Theory to Software. ( Cambridge Monographs on Applied and Computational Mathematics; Vol. 34). Cambridge: Cambridge University Press.
Kuipers, F., Gürsoy, U., & Kuznetsov, Y. (2019). Bifurcations in the RG-Flow of QCD. Journal of High Energy Physics, 2019(7), [75]. https://doi.org/10.1007/JHEP07(2019)075
Kalia, M., Kuznetsov, Y. A., & Meijer, H. G. E. (2019). Homoclinic saddle to saddle-focus transitions in 4D systems. Nonlinearity, 32(6), 2024-2054. https://doi.org/10.1088/1361-6544/ab0041
2018
Scholarly publications
Neirynck, N., Govaerts, W., Kuznetsov, Y. A., & Meijer, H. (2018). Numerical Bifurcation Analysis of Homoclinic Orbits Embedded in One-Dimensional Manifolds of Maps. ACM Transactions on Mathematical Software, 44(3), [25]. https://doi.org/10.1145/3134443
Al Hdaibat, B., Govaerts, W., van Kekem, D. L., & Kuznetsov, Y. A. (2018). Remarks on homoclinic structure in Bogdanov-Takens map. Journal of Difference Equations and Applications, 24(4), 575-587. https://doi.org/10.1080/10236198.2017.1329894
2017
Scholarly publications
Dijkstra, K., Kuznetsov, Y. A., van Puttem, M. J. A. M., & van Gils, S. A. (2017). A rate-reduced neuron model for complex spiking. The Journal of Mathematical Neuroscience, 7(13). https://doi.org/10.1186/s13408-017-0055-3
Neirynck, N., Govaerts, W., Kuznetsov, Y. A., & Meijer, H. (2017). Homoclinic orbits embedded in one-dimensional invariant manifolds of maps. In G. Stépán, & G. Csernák (Eds.), Proceedings of the 9th European Nonlinear Dynamics Conference [ID 149] CongressLIne Ltd.. http://congressline.hu/enoc2017/abstracts/149.pdf
Meijer, H., Govaerts, W., Kuznetsov, Y. A., & Neirycnk, N. (2017). A neutral homoclinic bifurcation in a 3D map. In G. Stépán, & G. Csernák (Eds.), Proceedings of the 9th European Nonlinear Dynamics Conference [ID 290] CongressLIne Ltd.. http://congressline.hu/enoc2017/pdf/ENOC2017_Front_matter.pdf
Bosschaert, M., Janssens, S. G., & Kuznetsov, Y. A. (2017). Switching to nonhyperbolic cycles from codim-2 bifurcations of equilibria in DDEs. In G. Stépán, & G. Csernák (Eds.), Proceedings of the 9th European Nonlinear Dynamics Conference [ID 276] CongressLIne Ltd..
2016
Scholarly publications
Neirynck, N., Al Hdaibat, B., Govaerts, W., Kuznetsov, Y. A., & Meijer, H. G. E. (2016). Using MatContM in the study of a nonlinear map in economics. In Journal of Physics: Conference Series (Vol. 692). [012013] IOP Publishing. https://doi.org/10.1088/1742-6596/692/1/012013
de Blank, H. J., Kuznetsov, Y. A., Pekkér, M. J., & Veldman, D. W. M. (2016). Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma. Physica D: Nonlinear Phenomena, 331, 13-26. https://doi.org/10.1016/j.physd.2016.05.008
Al Hdaibat, B., Govaerts, W., Kuznetsov, Y. A., & Meijer, H. G. E. (2016). Initialization of homoclinic solutions near Bogdanov-Takens points: Lindstedt-Poincaré compared with regular perturbation method. SIAM Journal on Applied Dynamical Systems, 15, 952-980. https://doi.org/10.1137/15M1017491
2015
Scholarly publications
Kuznetsov, Y. A., Meijer, H. G. E., Al Hdaibat, B., & Govaerts, W. (2015). Accurate approximation of homoclinic solutions in Gray-Scott kinetic model. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 25(9), [1550125].
Dijkstra, K., van Gils, S. A., Janssens, S. G., Kuznetsov, Y. A., & Visser, S. (2015). Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays. Physica D: Nonlinear Phenomena, 297, 88-101. https://doi.org/doi:10.1016/j.physd.2015.01.004
Bakri, T., Kuznetsov, Y., & Verhulst, F. (2015). Torus bifurcations in a mechanical system. Journal of Dynamics and Differential Equations, 27, 371-403. https://doi.org/10.1007/s10884-013-9339-9
2014
Scholarly publications
Kuznetsov, Y., Meijer, H., Al Hdaibat, B., & Govaerts, W. (2014). Improved homoclinic predictor for Bogdanov-Takens bifurcation. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 24(4), [1450057]. https://doi.org/10.1142/S0218127414500576
De Witte, V., Govaerts, W., Kuznetsov, Y., & Meijer, H. (2014). Analysis of bifurcations of limit cycles with Lyapunov exponents and numerical normal forms. Physica D: Nonlinear Phenomena, 269, 126-141. https://doi.org/10.1016/j.physd.2013.12.002
Bindel, D., Friedman, M., Govaerts, W., Hughes, J., & Kuznetsov, Y. (2014). Numerical computation of bifurcations in large equilibrium systems in MATLAB. Journal of Computational and Applied Mathematics, 261, 232-248. https://doi.org/10.1016/j.cam.2013.10.034
2013
Scholarly publications
van Gils, S. A., Janssens, S. G., Kuznetsov, Y., & Visser, S. (2013). On local bifurcations in neural field models with transmission delays. Journal of Mathematical Biology, 66(4-5), 837-887. https://doi.org/10.1007/s00285-012-0598-6
De Witte, V., Della Rossa, F., Govaerts, W., & Kuznetsov, Y. (2013). Numerical periodic normalization for codim 2 bifurcations of limit cycles: computational formulas, numerical implementation, and examples. SIAM Journal on Applied Dynamical Systems, 12(2), 722-788. https://doi.org/10.1137/120874904
Other output
Kuznetsov, Y. (2013). Exploring borders of chaos. University of Twente.
https://dspace.library.uu.nl/bitstream/handle/1874/314897/Oratieboekje_Kuznetsov.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/314897/Oratieboekje_Kuznetsov.pdf?sequence=1
2012
Scholarly publications
Bakri, T., Kuznetsov, Y., Verhulst, F., & Doedel, E. J. (2012). Multiple solutions of a generalized singular perturbed Bratu problem. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 24(4), [1250095]. https://doi.org/10.1142/S0218127412500952
De Witte, V., Govaerts, W., Kuznetsov, Y., & Friedman, M. (2012). Interactive initialization and continuation of homoclinic and heteroclinic orbits in MATLAB. ACM Transactions on Mathematical Software, 38(3), 1-34. https://doi.org/10.1145/2168773.2168776
Hommes, C., Kiseleva, T., Kuznetsov, Y., & Verbic, M. (2012). Is more memory in evolutionary selection (de)stabilizing? Macroeconomic Dynamics (paper), 16(3), 335-357.
https://dspace.library.uu.nl/bitstream/handle/1874/272645/HomKisKuzVerMarch2009.pdf?sequence=3
https://dspace.library.uu.nl/bitstream/handle/1874/272645/HomKisKuzVerMarch2009.pdf?sequence=3
2011
Scholarly publications
Dercole, F., Della Rossa, F., Colombo, A., & Kuznetsov, Y. (2011). Two degenerate boundary equilibrium bifurcations in planar Filippov systems. SIAM Journal on Applied Dynamical Systems, 10(4), 1525-1553.
https://dspace.library.uu.nl/bitstream/handle/1874/234101/cvips_doi_10.pdf?sequence=3
https://dspace.library.uu.nl/bitstream/handle/1874/234101/cvips_doi_10.pdf?sequence=3
Govaerts, W., Kuznetsov, Y., Meijer, H. G. E., & Neirynck, N. (2011). A study of resonance tongues near a Chenciner bifurcation using MatcontM. In D. Bernardini, G. Rega, & F. Romeo (Eds.), Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011) Sapienza, Università di Roma, Dipartimento di Ingegneria Strutturale e Geotecnica. https://doi.org/10.3267/ENOC2011Rome
2010
Scholarly publications
Kuznetsov, Y. (2010). 应用分支理论基础. Science Press.
2009
Scholarly publications
Doedel, E. J., Kooi, B. W., Voorn, G. A. K., & Kuznetsov, Y. (2009). Continuation of connecting orbits in 3D-ODE's (II) Cycle-to-cycle connections. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 19(1), 159-169.
Khoshsiar Ghaziani, R., Govaerts, W., Kuznetsov, Y., & Meijer, H. G. E. (2009). Numerical continuation of connecting orbits of maps in MATLAB. Journal of Difference Equations and Applications, 15(8-9), 849-875.
2008
Scholarly publications
Piiroinen, P. T., & Kuznetsov, Y. (2008). An event-driven method to simulate Filippov systems with accurate computing of sliding motions. ACM Transactions on Mathematical Software, 34(3).
Dhooge, A., Govaerts, W., Kuznetsov, Y., Meijer, H. G. E., & Sautois, B. (2008). New features of the software MatCont for bifurcation analysis of dynamical systems. Mathematical and Computer Modelling of Dynamcial Systems. Methods, Tools and Applications in Engineering and Related Sciences, 14(2), 147-175.
Doedel, E. J., Kooi, B. W., Voorn, G. A. K., & Kuznetsov, Y. (2008). Continuation of connecting orbits in 3D-ODEs. I. Point-to-cycle connections. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 18(7), 1889-1903.
Kuznetsov, Y., Meijer, H. G. E., Govaerts, W., & Sautois, B. (2008). Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs. Physica D: Nonlinear Phenomena, 237(23), 3061-3068.
2007
Scholarly publications
Govaerts, W., & Kuznetsov, Y. (2007). Interactive Continuation Tools. In B. Krauskopf, H. Osinga, & J. Galán-Vioque (Eds.), Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems (pp. 51-75). Springer-Canopus.
Govaerts, W., Khoshsiar Ghaziani, R., & Kuznetsov, Y. (2007). Numerical methods for two-parameter local bifurcation analysis of maps. SIAM journal on scientific computing, 29(6), 2644-2667.
2006
Scholarly publications
Kowalczyk, P., di Bernardo, M., Champneys, A. R., Hogan, S. J., Homer, M., Piiroinen, P. T., & Kuznetsov, Y. (2006). Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 16(3), 601-629.
Baer, S. M., Kooi, B. W., Kuznetsov, Y., & Thieme, H. R. (2006). Multiparametric bifurcation analysis of a basic two-stage population model. SIAM Journal on Applied Mathematics, 66(4), 1339-1365.
Kuznetsov, Y., & Meijer, H. G. E. (2006). Remarks on interacting Neimark-Sacker bifurcations. Journal of Difference Equations and Applications, 12(10), 1009-1035.
2005
Scholarly publications
Kuznetsov, Y., & Meijer, H. G. E. (2005). Numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues. SIAM journal on scientific computing, 26(6), 1932-1954.
Friedman, M., Govaerts, W., Kuznetsov, Y., & Sautois, B. (2005). Continuation of homoclinic orbits in MATLAB. In V. S. Sunderam, G. D. van Albada, P. M. A. Sloot, & J. J. Dongarra (Eds.), Proceedings of the International Conference on Computational Science 2005 (pp. 263-270). Springer.
Doedel, E. J., Govaerts, W., Kuznetsov, Y., & Dhooge, A. (2005). Numerical continuation of branch points of equilibria and periodic orbits. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 15(3), 841-860.
Govaerts, W., Kuznetsov, Y., & Dhooge, A. (2005). Numerical continuation of bifurcations of limit cycles in MATLAB. SIAM journal on scientific computing, 27(1), 231-252.
Bindel, D. S., Demmel, J. W., Friedman, M. J., Govaerts, W., & Kuznetsov, Y. (2005). Bifurcation analysis of large equilibrium systems in MATLAB. In V. S. Sunderam, G. D. van Albada, P. M. A. Sloot, & J. J. Dongarra (Eds.), Proceedings of the International Conference on Computational Science 2005 (pp. 50-57). Springer.
Kuznetsov, Y. (2005). Trends in bifurcations software: From CONTENT to MATCONT. In U. Kummer, J. Pahle, I. Surovtseva, & J. Zobeley (Eds.), Proceedings of the 4th Workshop on Computation of Biochemical Pathways and Genetic Networks (pp. 49-57). Logos Verlag.
Dercole, F., & Kuznetsov, Y. (2005). SlideCont: An AUTO97 driver for sliding bifurcation analysis. ACM Transactions on Mathematical Software, 31(1), 95-119.
Gonchenko, V. S., Kuznetsov, Y., & Meijer, H. G. E. (2005). Generalized Henon map and bifurcations of homoclinic tangencies. SIAM Journal on Applied Dynamical Systems, 4(2), 407-436.
Kuznetsov, Y., Govaerts, W., Doedel, E. J., & Dhooge, A. (2005). Numerical periodic normalization for codim 1 bifurcations of limit cycles. SIAM Journal on Numerical Analysis, 43(4), 1407-1435.
Dhooge, A., Sautois, B., Govaerts, W., & Kuznetsov, Y. (2005). MatCont: Matlab Software for Bifurcation Study of Dynamical Systems. In T. E. Simos, G. Psihoyios, & C. Tsitouras (Eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2005 (pp. 838-841). Wiley.
2004
Scholarly publications
Dhooge, A., Govaerts, W., & Kuznetsov, Y. (2004). Numerical continuation of branch points of limit cycles in MATCONT. In Proceedings of the International Conference on Computational Science ICCS 2004, Part II (pp. 42-49)
Kuznetsov, Y., Meijer, M. G. E., & van Veen, L. (2004). The fold-flip bifurcation. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 14, 2253-2282.
2003
Scholarly publications
Dhooge, A., Govaerts, W., & Kuznetsov, Y. (2003). MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Transactions on Mathematical Software, 29(2), 141-164.
Dhooge, A., Govaerts, W., & Kuznetsov, Y. (2003). Numerical continuation of fold bifurcations of limit cycles in MATCONT. In P. M. A. Sloot, D. Abramson, & A. V. Bogdanov (Eds.), Proceedings of the International Conference on Computational Science ICCS 2003, Part I (pp. 701-710). Springer.
Dhooge, A., Govaerts, W., Kuznetsov, Y., Mestrom, W., & Riet, A. M. (2003). Cl_matcont: a continuation toolbox in Matlab. In Proceedings of the 2003 ACM Symposium on Applied Computing (pp. 161-166). ACM Press.
Kuznetsov, Y., Rinaldi, S., & Gragnani, A. (2003). One-parameter bifurcations in planar Filippov systems. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 13(8), 2157-2188.
Doedel, E. J., Govaerts, W., & Kuznetsov, Y. (2003). Computation of periodic solution bifurcations in ODEs using bordered systems. SIAM Journal on Numerical Analysis, 41(2), 401-435.
Dercole, F., Gragnani, A., Kuznetsov, Y., & Rinaldi, S. (2003). Numerical sliding bifurcation analysis: An application to a relay control system. IEEE Transaction on circuits and systems part 1 Fundamental theory and applications, 50(8), 1058-1063.
2002
Scholarly publications
Beyn, W-J., Champneys, A. R., Govaerts, W., Kuznetsov, Y., & Sandstede, B. (2002). Numerical Computation, and Computation of Normal Forms. In B. Fiedler (Ed.), Handbook of Dynamical Systems (pp. 149-219). Elsevier Science.
Other output
Kuznetsov, Y. (Author). (2002). SlideCont. Software
Kuznetsov, Y. (2002). Codimension - 1 bifurcations in planar Filippov systems. Workshop "Bifurcations in Nonsmooth Dynamical Systems", Milaan, Italië.
2001
Scholarly publications
Kuznetsov, Y., De Feo, O., & Rinaldi, S. (2001). Belyakov homoclinic bifurcations in a tritrophic food chain model. SIAM Journal on Applied Mathematics, 62, 462-487.
2000
Scholarly publications
Govaerts, W., Kuznetsov, Y., & Sijnave, B. (2000). Continuation of codimension-2 equilibrium bifurcations in CONTENT. In E. Doedel, & L. S. Tuckerman (Eds.), Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems (pp. 163-184). Springer.
Govaerts, W., Kuznetsov, Y., & Sijnave, B. (2000). Numerical methods for the generalized Hopf bifurcation. SIAM Journal on Numerical Analysis, 38(1), 329-346.
Scheffer, M., Rinaldi, S., & Kuznetsov, Y. (2000). Effects of fish on plankton dynamics: a theoretical analysis. Canadian Journal of Fisheries and Aquatic Sciences, 57, 1208-1219.
Professional publications
Kuznetsov, Y. (2000). NLDV Computer Sessions, Academic year 1999-2000. UU WINFI Wiskunde.
Other output
Kuznetsov, Y. (Author). (2000). MATLAB Continuation Toolbox (http://www.math.uu.nl/people/kuznet). Software, .
1999
Scholarly publications
Kuznetsov, Y. (1999). Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODES. SIAM Journal on Numerical Analysis, 36, 1104-1124.
Govaerts, W., Kuznetsov, Y., & Sijnave, B. (1999). Bifurcations of maps in the software package CONTENT. In V. G. Ganzha, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing (pp. 191-206). Springer.
1998
Scholarly publications
Kuznetsov, Y. (1998). Elements of applied bifurcation theory. (2 ed.) (Applied Mathematical Sciences; Vol. 112). Springer.