Politechnika Wrocławska, Wydział Matematyki
Email: piotr.s.kowalczyk@pwr.edu.pl


Adres: Budynek C19, pokój A.3.19, ul. HoeneWrońskiego 13C, 50376 Wrocław Konsultacje: Poniedziałek 14:3016:30 Piątek 10:0012:00 
Dynamics of piecewisesmooth and
hybrid systems
Biped dynamics, human balance and human locomotion
Dynamics of piecewisesmooth systems with time
delay
M. di Bernardo, C. Budd, A. R. Champneys, P. Kowalczyk, Piecewisesmooth Dynamical Systems: Theory and Applications (2008) (see Springer).
[29] M. Desroches P. Kowalczyk, and S. Rodrigues, Discontinuity induced dynamics in ConductanceBased Adaptive Exponential IntegrateandFire Model, submitted for publication to Bulletin of Mathematical Biology, February 2024
[28] Zofia Wróblewska, P. Kowalczyk, and Łukasz Płociniczak, Nonexistence of asymmetric solutions of human running gaits in a switched inverted pendulum model, accepted for publication to Mathematica Applicanda, February 2024
[27] Zofia Wróblewska, P. Kowalczyk, and Krzysztof Przednowek, Leg stiffness and energy minimization in human running gaits, Sports Engineering, accepted for publication, April 2024
[26] Zofia Wróblewska, P. Kowalczyk, and Łukasz Płociniczak, Stability of fixed points in an approximate solution of the springmass running model, accepted for publication in the IMA Journal of Applied Mathematics, March 2023
[22] P. Kowalczyk, A novel route to a Hopfbifurcation scenario in switched systems with dead zone, Physica D, Vol. 348, pp. 6066, 2017
[21] S. Nema, P. Kowalczyk, I. Loram, Waveletfrequency analysis for the detection of discontinuities in switched system models of human balance, Human Movement Science, 2016
[20] P. Glendinning, P. Kowalczyk, and A. B. Nordmark, Multiple attractors in grazingsliding bifurcations in Filippov type flows, the IMA Journal of Applied Mathematics, 2016
[19] S. Nema, P. Kowalczyk, and I. Loram, Complexity and dynamics of switched human balance during quiet standing, Biological Cybernetics, 2015
[18] S. Nema, P. Kowalczyk, Detecting abrupt changes in a noisy Van der Pol type oscillator, Differential Equations and Dynamical Systems, 2015
[17] P. Kowalczyk, S. Nema, P. Glendinning, I. Loram and M. Brown, ARMA analysis of linear and discontinuous models of human balance during quiet standing, Chaos: An Interdisciplinary Journal of Nonlinear Science, June 2014
[16] P. Glendinning, P. Kowalczyk, and A. B. Nordmark, Attractors near grazingsliding bifurcations, Nonlinearity, Vol 25(6), pp. 1867 1885, 2012
[15] P. Kowalczyk, P. Glendinning, Martin Brown, Gustavo MedranoCerda, Houman Dallali, and Jonathan Shapiro Modelling human balance using switched systems with linear feedback control, In Print, Interdiscpilinary Journal of the Royal Society Interface, Available online 21 June 2011
[14] P. Kowalczyk, P. Glendinning Boundaryequilibrium bifurcations in piecewisesmooth slowfast systems, Chaos: An interdisciplinary Journal of Nonlinear Science, June 2011
[13] P. Glendinning, P. Kowalczyk, Microchaotic dynamics due to digital sampling in hybrid systems of Filippov type, Physica D, 239(12), pp.5871, (2010)
[12] J. Sieber, P. Kowalczyk, Smallscale instabilities in dynamical systems with sliding, Physica D, 239(12), pp. 4457, 2010
[11] J. Sieber, P. Kowalczyk, S.J. Hogan, M. di Bernardo: Dynamics of symmetric dynamical systems with delayed switching. Special Issue of Journal of Vibration and Control on Dynamics and Control of Systems with TimeDelay, Vol. 16(78), 2010
[10] P. Glendinning, P. Kowalczyk, Dynamics of a hybrid thermostat model with discrete sampling time control, Dynamical Systems, 24(3), pp. 343360, 2009
[9] M. di Bernardo, C. Budd, A. R. Champneys, P. Kowalczyk, A. B. Nordmark, G. Olivar and P.T. Piiroinen, Bifurcations in Nonsmooth Dynamical Systems, SIAM Review, 50(4), pp.629701, 2008
[8] A. Colombo, M. di Bernardo, J. Hogan and P. Kowalczyk, Complex dynamics in a relay feedback system with hysteresis and delay, Journal of Nonlinear Science, 17(2), pp. 85108, 2007
[7] P. Kowalczyk, P.T. Piiroinen, Twoparameter sliding bifurcations of periodic solutions in a dryfriction oscillator, Physica D, 237(8), pp.10531073, 2007
[6] A. B. Nordmark and P. Kowalczyk, A codimensiontwo scenario of sliding solutions in grazingsliding bifurcations,, Nonlinearity 19(1) pp. 126, 2006)
[5] P. Kowalczyk, M. di Bernardo, A. R. Champneys, S. J. Hogan, M. Homer, Yu. A. Kuznetsov, A. B. Nordmark and P. T. Piiroinen, Twoparameter nonsmooth bifurcations of limit cycles: classification and open problems, International Journal of bifurcation and chaos, Vol. 16 No. 3, pp.601629, 2006
[4] P. Kowalczyk and M. di Bernardo, Twoparameter degenerate sliding bifurcations in Filippov systems, Physica D, Vol. 204 pp. 204  229, 2005
[3] P. Kowalczyk, Robust chaos and bordercollision bifurcations in noninvertible piecewiselinear maps, Nonlinearity, Vol. 18 pp. 485504, 2005
[2] M. di Bernardo, P. Kowalczyk, and A. B. Nordmark, Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dryfriction oscillators, International Journal of Bifurcation and Chaos, Vol. 13, No. 10 pp. 29352948, 2003
[1] M. di Bernardo, P. Kowalczyk, and A. B. Nordmark, Bifurcations of dynamical systems with sliding: derivation of normalform mappings, Physica D, volume 170, pp. 175205, 2002
P. Kowalczyk, P. Glendinning, Microchaos in Relay Feedback Systems with BangBang Control and Digital Sampling, To appear in the proceedings of 18th Word Congress of the International Federation of Automatic Control, Milan 2011
P. Kowalczyk, J. Sieber, Robustness of grazingsliding bifurcations in Filippov type systems, In the proceedings of Second IFAC meeting related to analysis and control of chaotic systems, London 2009
P. Kowalczyk, A. B. Nordmark,
Bifurcations in nonsmooth models of
mechanical systems, In the proceeding of EUROMECH 500
conference on Nonsmooth Problems in Vehicle Systems Dynamics 
Analysis and Solutions, Lingby, Denmark 2008
P. Kowalczyk, Grazing bifurcations: A mechanism for the sudden onset of robust chaos, In the proceedings of 10th Experimental Chaos Conference, Catania, Italy 2008
Samia K. Genena, Daniel J. Pagano and P. Kowalczyk: HOSM Control of StickSlip Oscillations in Oil Well Drillstrings,in Proceeding to European Control Conference Kos 2007
J. Sieber, P. Kowalczyk: Symmetric event collisions in dynamical systems with delayed switches . To appear in a special issue of "Discrete and Continuous Dynamical Systems Series B" (Proceedings of the sixth AIMS Conference on Dynamical Systems, Differential Equations and Applications, Poitiers 2007
M. di Bernardo, A.R. Champneys, P. Kowalczyk, CornerCollision and GrazingSliding: practical examples of bordercollision bifurcations, Proc. IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, Kluwer Academic, 2003
M. di Bernardo and P. Kowalczyk, On the existence of stable asymmetric limit cycles and chaos in unforced symmetric relay feedback system, in Proceeding to European Control Conference Porto 2001
P. Kowalczyk and M. di Bernardo, On a novel class of bifurcations in hybrid dynamical systems – the case of relay feedback system, in Proceedings of 4th International Workshop on Hybrid Systems Computation and Control, published by SpringerVerlag, pp. 361374, 2001
A. Sowa and P. Kowalczyk, Test chamber characteristics – an important factor determining required RF power of amplifier in radiated immunity tests, Accepted for the Electromagnetic Compatibility Conference Wroclaw 2000, Poland