Publicationlist of Yuri A. Kuznetsov.

Books:

Kuznetsov, Yu.A.
Elements of Applied Bifurcation Theory.
Springer-Verlag, New York, 1995,1998, 2004
Science Press, Beijing, 2010 [translation into Chinese]

Bazykin, A.D., Kuznetsov, Yu.A., and Khibnik, A.I.
Portraits of Bifurcations: Bifurcation Diagrams of Planar Dynamical Systems.
Znanie, Moscow, 1989 [in Russian]
(Reprinted as Appendix 1 to Bazykin, A.D. Nonlinear Dynamics of Interacting Populations, ICS, Izhevsk, 2003 [in Russian], pp. 261-342)



Papers:

de Blank, H. J.,  Kuznetsov, Yu. A., Pekkér, M. J., and Veldman, D. W. M.
Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma.
Phys. D 331 (2016), 13-26.


Al-Hdaibat, B.,  Govaerts, W.,  Kuznetsov, Yu. A., and  Meijer, H. G. E.
Initialization of homoclinic solutions near Bogdanov-Takens points: Lindstedt-Poincaré compared with regular perturbation method.
SIAM J. Appl. Dyn. Syst. 15 (2016), 952-980

Bakri, T., Kuznetsov, Yu.A., and Verhulst, F.

Torus
bifurcations in a mechanical system.
J. Dyn. Diff.  Equat. 27 (2015), 371-403


Kuznetsov, Yu.A., Meijer, H.G.E., Al  Hdaibat, B., and Govaerts, W.

Accurate approximation of homoclinic solutions in Gray-Scott kinetic model.
Int. J. Bifurcation & Chaos 25 (2015), 1550125 (10 pages)

Dijkstra, K., Gils, S.A. van, Janssens, S.G., Kuznetsov, Yu.A., and Visser, S.
Pitchfork-Hopf bifurcations in 1D neural field models with transmission delays.
Physica D 297 (2015), 88-101

Kuznetsov, Yu.A., Meijer, H.G.E., Al  Hdaibat, B., and Govaerts, W.
Improved homoclinic predictor for Bogdanov-Takens bifurcation.
Int. J. Bifurcation & Chaos 24 (2014), 1450057 (12 pages)

De Witte, V., Govaerts, W., Kuznetsov, Yu.A., and Meijer, H. G. E.
Analysis of bifurcations of limit cycles with Lyapunov exponents and numerical normal forms.
Physica D 269 (2014), 126-141

Bindel, D.,  Friedman, M., Govaerts, Hughes, J., and Kuznetsov, Yu.A.
Numerical computation of bifurcations in large equilibrium systems in MATLAB.
J. Comp. Appl. Math., 261 (2014), 232-248

De Witte, V., Della Rossa, F., Govaerts, W., and Kuznetsov, Yu.A.
Numerical periodic normalization for codim 2 bifurcations of limit cycles: Computational formulas, numerical implementation, and examples.
SIAM J. Appl. Dyn. Syst. 12 (2013), 722-788

Gils, S.A. van, Janssens, S.G., Kuznetsov, Yu.A., and Visser, S.
On local bifurcations in neural field models with transmission delays.
J. Math. Biology, 66 (2013), 837-887

Hommes, C., Kiseleva, T., Kuznetsov, Yu., and Verbic, M.
Is more memory in evolutionary selection (de)stabilizing?
Macroeconomic Dynamics, 16 (2012), 335-357

De Witte, V., Govaerts, W., Kuznetsov Yu.A., and Friedman, M.
Interactive initialization and continuation of homoclinic and heteroclinic orbits in MATLAB.
ACM Trans. Math. Software 38 (2012), 18:1-18:34

Bakri T., Kuznetsov, Yu.A., Verhulst, F. and Doedel, E.
Multiple solutions of a generalized singular perturbed Bratu problem.
Int. J. Bifurcation & Chaos 24:4 (2012) 1250095 (10 pages)

Dercole, F., Della Rossa, F., Colombo, A., and Kuznetsov, Yu.A.
Two degenerate boundary equilibrium bifurcations in planar Filippov systems.
SIAM J. Appl. Dyn. Sys. 10 (2011), 1525-1553

Khoshsiar Ghaziani, R., Govaerts, W., Kuznetsov, Yu.A., and Meijer, H. G. E.
Numerical continuation of connecting orbits of maps in MATLAB.
Journal of Difference Equations and Applications, 15 (2009), 849-875

Doedel, E.J., Kooi, B.W., van Voorn, G.A.K. , and Kuznetsov, Yu.A.
Continuation of connecting orbits in 3D-ODEs: (II) Cycle-to-cycle connections.
Int. J. Bifurcation & Chaos 19 (2009), 159-169

Kuznetsov, Yu.A., Meijer,  H.G.E., Govaerts, W., and Sautois, B.
Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs.
Physica D 237 (2008), 3061-3068

Doedel, E.J., Kooi, B.W., van Voorn, G.A.K. , and Kuznetsov, Yu.A.
Continuation of connecting orbits in 3D-ODEs: (I) Point-to-cycle connections.
Int. J. Bifurcation & Chaos 18 (2008), 1889-1903

Piiroinen, P.T. and Kuznetsov, Yu.A.
An event-driven method to simulate Filippov systems with accurate computing of sliding motions.
ACM Trans. Math. Software 34 (2008), 13:1-13:24

Dhooge, A. , Govaerts, W.,  Kuznetsov, Yu.A.,  Meijer, H.G.E.,  and  Sautois, B.
New features of the software MatCont for bifurcation analysis of dynamical systems.
Mathematical and Computer Modelling of Dynamical Systems 14 (2008), 145-175

Govaerts, W., Khoshsiar Ghaziani, R., Kuznetsov, Yu.A., and Meijer, H.G.E.
Numerical methods for two-parameter local bifurcation analysis of maps.
SIAM J. Sci. Comp. 29 (2007), 2644-2667

Aponin, Yu.M., Aponina, E.A., and Kuznetsov, Yu.A.
Mathematical modelling of spatial and temporal dynamics of a plant population with age structure.
Mathematical Biology and Bioinformatics 1 (2006), 1-16 [in Russian]

Kuznetsov, Yu.A. and Meijer, H.G.E.
Remarks on  interacting Neimark-Sacker bifurcations.
Journal of Difference Equations and Applications 12 (2006), 1009-1035

Kowalczyk, P., di Bernardo, M., Champneys, A. R., Hogan, S. J., Homer, M., Piiroinen, P. T., Kuznetsov, Yu. A., and Nordmark, A.
Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems.
Int. J. Bifurcation & Chaos 16 (2006), 601-629

Baer, S.M., Kooi, B.W., Kuznetsov, Yu.A., and Thieme, H.R.
Multiparametric bifurcation analysis of a basic two-stage population model.
SIAM J. Appl. Math. 66 (2006), 1339-1365

Kuznetsov, Yu.A.
Practical computation of normal forms on center manifolds at degenerate Bogdanov-Takens bifurcations.
Int. J. Bifurcation & Chaos 15 (2005), 3535-3546

Kuznetsov, Yu. A. , Govaerts, W. , Doedel, E. J., and Dhooge, A.
Numerical periodic normalization for codim 1 bifurcations of limit cycles.
SIAM J. Numer. Anal. 43 (2005), 1407-1435

Govaerts, W., Kuznetsov, Yu.A., and Dhooge, A.
Numerical continuation of bifurcations of limit cycles in MATLAB.
SIAM J. Sci. Comp. 27 (2005), 231-252

Doedel, E.J., Govaerts, W., Kuznetsov, Yu.A., and Dhooge, A.
Numerical continuation of branch points of equilibria and periodic orbits.
Int. J. Bifurcation & Chaos 15 (2005), 841-860

Kuznetsov,Yu.A. and Meijer H.G.E.
Numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues.
SIAM J. Sci. Comp. 26 (2005), 1932-1954

Gonchenko, V.S. , Kuznetsov,Yu.A., and Meijer H.G.E.
Generalized Hénon map and bifurcations of homoclinic tangencies.
SIAM J. Appl. Dyn. Sys. 4 (2005), 407-436

Dercole, F. and Kuznetsov, Yu.A.
SlideCont: An AUTO97 driver for sliding bifurcation analysis.
ACM Trans. Math. Software 31 (2005), 95-119

Kuznetsov, Yu.A., Meijer, H.G.E., and van Veen, L.
The fold-flip bifurcation.
Int. J. Bifurcation & Chaos 14 (2004), 2253-2282

Kuznetsov, Yu.A., Rinaldi, S., and Gragnani, A.
One-parameter bifurcations in planar Filippov systems.
Int. J.  Bifurcation & Chaos 13 (2003), 2157-2188

Dercole,  F., Gragnani, A., Kuznetsov, Yu.A., and Rinaldi, S.
Numerical  sliding bifurcation analysis: An application to a relay control system.
IEEE Trans. Circuit Systems - I: Fund. Theory Appl. 50 (2003), 1058-1063

Doedel, E.J., Govaerts, W., and Kuznetsov, Yu.A.
Computation of periodic solution bifurcations in ODEs using bordered systems.
SIAM J. Numer. Anal. 41 (2003), 401-435

Dhooge, A., Govaerts,  W., and  Kuznetsov, Yu.A.
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs.
ACM Trans. Math. Software  29 (2003), 141 - 164

Kuznetsov, Yu.A., De Feo, O., and Rinaldi, S.
Belyakov homoclinic bifurcations in a tritrophic food chain model.
SIAM J. Appl. Math. 62 (2001), 462-487

Govaerts, W., Kuznetsov, Yu.A., and Sijnave, B.
Numerical methods for the generalized Hopf bifurcation.
SIAM J. Numer. Anal. 38 (2000), 329-346

Scheffer, M., Rinaldi, S., and Kuznetsov, Yu.A.
Effects of fish on plankton dynamics: a theoretical analysis.
Can. J. Fish. Aquat. Sci. 57 (2000), 1208-1219

Kuznetsov, Yu.A.
Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODEs.
SIAM J. Numer. Anal. 36 (1999), 1104-1124

Govaerts, W., Kuznetsov, Yu.A., and Sijnave, B.
Implementation of Hopf and double Hopf continuation using bordering methods.
ACM Trans. Math. Software 24 (1998), 418-436

Scheffer, M., Rinaldi, S., Kuznetsov, Yu.A., and van Nes, E.H.
Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system.
Oikos 80 (1997), 519-532

Champneys, A.R., Kuznetsov, Yu.A., and Sandstede, B.
A numerical toolbox for homoclinic bifurcation analysis.
Int. J. Bifurcation & Chaos 6 (1996), 867-887

Kuznetsov, Yu.A. and Rinaldi, S.
Remarks on food chain dynamics.
Math. Biosciences 134 (1996), 1-33

Kuznetsov, Yu.A., Muratori, S., and Rinaldi, S.
Homoclinic bifurcations in slow-fast second order systems.
Nonlinear Analysis 25 (1995), 747-762

Champneys, A.R. and Kuznetsov, Yu.A.
Numerical detection and continuation of codimension-two homoclinic bifurcations.
Int. J. Bifurcation & Chaos 4 (1994), 795-822

Kuznetsov, Yu.A. and Piccardi, C.
Bifurcations and chaos in a periodically forced prototype adaptive control system.
Kybernetika 30 (1994), 121-128

Kuznetsov, Yu.A., Antonovsky, M.Ya.,Biktashev, V.N., and Aponina, E.A.
A cross-diffusion model of forest boundary dynamics.
J. Math. Biol. 32 (1994), 219-132

Kuznetsov, Yu.A. and Piccardi, C.
Bifurcation analysis of periodic SEIR and SIR epidemic models.
J. Math. Biol. 30 (1994), 109-121

Ghezzi, L.L. and Kuznetsov, Yu.A.
Strong resonances and chaos in a stock market model.
Int. J. Systems Sci. 11 (1994), 1941-1955

Kuznetsov, Yu.A.
Impulses of complicated form in models of nerve conduction.
Selecta Math. Sovetica 13 (1994), 128-142

Doveri, F., Scheffer, M., Rinaldi, S., Muratori, S., and Kuznetsov, Yu.A.
Seasonality and chaos in a plankton-fish model.
Theor. Pop. Biol. 43 (1993), 159-183

Khibnik, A.I., Kuznetsov, Yu.A., Levitin, V.V., and Nikolaev, E.V.
Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps.
Physica D 62 (1993), 360-371

Rinaldi, S., Muratori, S., and Kuznetsov, Yu.A.
Multiple attractors, catastriphes and chaos in seasonally perturbed predator-prey communities.
Bull. Math. Biol. 55 (1993), 15-35

Kuznetsov, Yu.A., Muratori, S., and Rinaldi, S.
Bifurcations and chaos in a periodic predator-prey model.
Int. J. Bifurcation & Chaos 2 (1992), 117-128

Kuznetsov, Yu.A. and Rinaldi, S.
Numerical analysis of the flip bifurcation of maps.
Appl. Math. Comp. 43 (1991), 231-236

Antonovsky, M.Ya., Fleming, R.A., Kuznetsov, Yu.A., and Clark, W.C.
Forest-pest interaction: The simplest mathematical models.
Theor. Pop. Biol. 37 (1990), 343-367

Bazykin, A.D., Berezovskaya, F.S., Denisov, G.A., and Kuznetsov, Yu.A.
The influence of predator saturation effect and competition among predators on predator-prey dynamics.
Ecol. Modelling 14 (1981), 39-57


In Proceedings/Collections:


Neirynck, N., Al-Hdaibat, B., Govaerts, W. , Kuznetsov, Yu. A. , and Meijer, H. G. E.
Using MatContM in the study of a nonlinear map in economics.
Journal of Physics: Conference Series 692 (2016) 012013

Govaerts, W. , Kuznetsov, Yu. A. , Meijer, H. G. E. , and Neirynck, N.

A study of resonance tongues near a Chenciner bifurcation using MatcontM
In: "Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)", 24-29 July 2011, Rome, Italy, MS-03-7

De Witte, V., Govaerts, W., and Kuznetsov Yu.A.

Numerical implementation of a homotopy method for computing homoclinic and heteroclinic orbits.
In: "Proceedings of the 16th US National Congress of Theoretical and Applied Mechanics USNCTAM2010", June 27-July 2, 2010, State College, PA, USA, USNCTAM2010-455

Govaerts, W., and Kuznetsov, Yu.A.
Interactive Continuation Tools.
In: B. Krauskopf et al.  (eds.)  "Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems", Springer-Canopus (2007), 51-75.

Dhooge, A., Sautois, B., Govaerts, W., and Kuznetsov, Yu.A.
MatCont: Matlab Software for Bifurcation Study of Dynamical Systems.
In: T.E. Simos et al.  (eds.)  "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics ICNAAM 2005, 16-20 September 2005, Rodes, Greece", Wiley-VCH (2005), 838-841.

Kuznetsov, Yu.A.
Trends in bifurcation software: From CONTENT to MATCONT.
In: U. Kummer et al. (eds.) "Proceedings of the 4th Workshop on Computation of Biochemical Pathways and Genetic Networks", Villa Bosch, Heidelberg, September 12-13, 2005. Logos Verlag Berlin, 49-57

Bindel, D.S., Demmel, J.W., Friedman, M.J., Govaerts, W.J.F., and Kuznetsov, Yu.A.
Bifircation analysis of large equilibrium systems in MATLAB.
In: V.S. Sunderam et al. (eds.) "Proceedings of the International Conference on Computational Science ICCS 2005, Atlanta, GA, USA, May 22-25, 2005, Part I". Springer Verlag Lecture Notes in Computer Science  3514 (2005), 50-57

Friedman, M., Govaerts, W., Kuznetsov, Yu.A., and Sautois, B.
Continuation of homoclinic orbits in MATLAB.
In: V.S. Sunderam et al. (eds.) "Proceedings of the International Conference on Computational Science ICCS 2005, Atlanta, GA, USA, May 22-25, 2005, Part I". Springer Verlag Lecture Notes in Computer Science  3514 (2005), 263-270

Dhooge, A., Govaerts, W. and Kuznetsov, Yu.A.
Numerical continuation of branch points of limit cycles in MatCont.
In: Bubak, M.; Albada, G.D.v.; Sloot, P.M.A.; Dongarra, J.J. (eds.) "Proceedings of the International
Conference on Computational Science ICCS 2004, Krakow, Poland, 6-9 June 2004, Part II". Springer Verlag Lecture Notes in Computer Science 3037, 2004 (May 2004),  42-49

Dhooge, A., Govaerts, W., and Kuznetsov, Yu.A.
Bifurcations of Periodic Solutions of ODEs using Bordered Systems.
In: G. Psihoyios (ed.)  "Proceedings of the International Conference on Numerical Analysis and Computational Mathematics ICNAAM 2003, Anglia Polytechnic University, 23-26 May 2003, Cambridge, UK", J. Wiley (2003), 61-64.

Dhooge, A., Govaerts, W., and Kuznetsov, Yu.A.
Numerical continuation of fold bifurcations of limit cycles in MATCONT.
In: P.M.A. Sloot et al. (eds.) "Proceedings of the International Conference on Computational Science ICCS 2003, Melbourne, Australia and St Petersburg, Russia, 2-4 June 2003, Part I". Springer Verlag Lecture Notes in Computer Science  2657 (May 2003), 701-710

Dhooge, A., Govaerts, W., Kuznetsov, Yu.A., Mestrom, W., and Riet, A.M.
Cl_matcont: A continuation toolbox in Matlab.
In:  "Proceedings of the 2003 ACM Symposium on Applied Computing" (Melbourne, Florida, USA, March 2003), 161-166  (PDF)

Beyn, W.-J., Champneys, A., Doedel, E., Govaerts, W., Kuznetsov, Yu.A., and Sandstede, B.
Numerical continuation, and computation of normal forms.
In: B. Fiedler (ed.) "Handbook of Dynamical Systems", v.2, Elsevier Science, North-Holland, 2002,  149-219

Govaerts, W., Kuznetsov, Yu.A., and Sijnave, B.
Continuation of codimension-2 equilibrium bifurcations in CONTENT.
In: Doedel, E. and Tickerman, L.S. (eds.) "Numerical methods for Bifurcation Problems and Large-Scale Dynamical Systems", Springer-Verlag, New York, 2000,  163-184

Govaerts, W., Kuznetsov, Yu.A., and Sijnave, B.
Bifurcations of maps in the software package CONTENT.
In: Ganzha, V.G, Mayr, E.W., and Vorozhtsov, E.V. (eds.) "Computer Algebra in Scientific Computing", Springer-Verlag, New York, 1999,  191-206

Kuznetsov, Yu.A.
Centere manifold. Codimension-two bifurcations. Equivalence of dynamical systems. Homoclinic bifurcations. Hopf bifurcation. Saddle-node bifurcation.
In: Hazewinkel, M. (ed.) "Encyclopaedia of Mathematics", Supp. vol. I, Kluwer Academic Publishers, The Netherlands, 1997, 179-181, 190-191, 240, 293-294, 296-297, 444-445

Kuznetsov, Yu.A.
Numerical analysis of the orientability of homoclinic trajectories.
Int. Ser. Numer. Math. 97, 1991, 237-242

Kuznetsov, Yu.A.
Computation of invariant manifold bifurcations.
In: Roose, D., de Dier, B., and Spence, A. (eds.) "Continuation and Bifurcations: Numerical Thechniques and Applications", Kluwer Academic Publishers, The Netherlands, 1990, 183-195



Book reviews:

Kuznetsov, Yu.A.
Bifurcation Theory: An Introduction with Applications to PDEs (by Hansjorg Kielhöfer).
SIAM Review 47 (2005), 176-178


Manuals/Readers:


Kuznetsov, Yu.A. and Hanssmann, H.
Basis Differentiaalvergelijkingen.
Departement Wiskunde, Universiteit Utrecht, The Netherlands (2011-) [in Dutch]

Kuznetsov, Yu.A., Stienstra, J.

Fouriertheorie.
Departement Wiskunde, Universiteit Utrecht, The Netherlands (2009) [in Dutch]

Kuznetsov, Yu.A.
Basis Differentiaalvergelijkingen.
Departement Wiskunde, Universiteit Utrecht, The Netherlands (2006-2010) [in Dutch]

Kuznetsov, Yu.A., Lemmens, P.W.H., Maintz, J.B.A., Tel, G.
Wiskunde voor Informatici.
Dictaat, Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, The Netherlands (2003)  [in Dutch]

Dercole, F. and Kuznetsov, Yu.A.
SlideCont: An AUTO97 driver for sliding bifurcation analysis.
Preprint nr. 1261, Department of Mathematics, Universiteit Utrecht, The Netherlands (2002)

Kuznetsov, Yu.A.
NLDV Computer sessions. Academic year 1999-2000.
Mathematical Institute, Utrecht University, The Netherlands (2000)

Kuznetsov, Yu.A.
CONTENT - integrated environment for analysis of dynamical systems. Tutorial.
Ecole Normale Superieure de Lyon, Rapport de Recherche UPMA-98-224 (1998)

Doedel, E., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Yu.A., Sandstede, B., and Wang X.-J.
AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont).
User's Guide. Concordia University, Montreal, Canada (1997)

Champneys, A.R., Kuznetsov, Yu.A., and Sandstede, B.
HomCont: An AUTO86 driver for homoclinic bifurcation analysis.
Report AM-R9516, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands (1995)

Khibnik, A.I., Kuznetsov, Yu.A., Levitin, V.V., and Nikolaev, E.V.
Interactive LOCal BIFurcation Analyzer: LOCBIF, v. 2.
Computer Algebra Nederland Expertise Center, Amsterdam, The Netherlands (1993)

Kuznetsov, Yu.A.
One-dimensional invariant manifolds of ODE-systems depending upon parameters.
FORTRAN Software Series, 8, Research Computing Centre, USSR Academy of Sciences, Pushchino, Moscow Region (1983) [in Russian]


Preprints:

Kuznetsov, Yu.A., Levitin, V.V., and Skovoroda A.R.

Continuation of stationary solutions to evolution problems in CONTENT.
Report AM-R9611, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands (1996)

Antonovsky, M.Ya., Kuznetsov, Yu.A., and Clark, W.
The influence of pests on forest age structure dynamics: The simplest mathematical models.
IIASA Working Paper WP-87-70, International Institute for Applied Systems Analysis, Laxenburg, Austria (1987)

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Last updated: Oct 10, 2014

kuznet@math.uu.nl