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Piotr Kowalczyk - Personal Homepage

Research Associate in the School of Mathematics (member of CICADA), University of Manchester

Profile2.jpg Email: piotr.kowalczyk@manchester.ac.uk
Office address: Alan Turing Building,
School of Mathematics,
University of Manchester,
Oxford Road,
Manchester M13 9PL, U.K.

Tel. : +44 (0) 161 306 3214, Fax: +44 (0) 161 275 5819

Research interests

Dynamics of piecewise-smooth and hybrid systems

  • 1) Dynamical systems theory with an emphasis on the analysis and computations of bifurcations in non-smooth dynamical systems
  • 2) Engineering applications of dynamical systems. For instance understanding the phenomena brought about by the presence of discontinuous nonlinearities in mechanical systems with dry-friction, preload, impacts, hysteresis, and saturation. Other applications of interest are power electronics and hybrid systems.
  • 3) Experimental non-smooth dynamics. The next step in the theory of non-smooth systems is to bring the developed tools that are used to make analytical and numerical investigations of mathematical models close to real life applications. See continuation for experiments in links below.
  • 4) Robustness of discontinuity induced bifurcations and singularly perturbed pieceiwse-smooth systems. It is important to understand how small imperfections that are usually ignored by the modeler influence system dynamics. For instance, in the context of modelling DC/DC power converters there are small capacitances or inductances that are ignored. The question araises how and if these produce some significant effects on the system dynamics.
  • 5) Dynamics of complex networks with evolving topology.
    Links:

    • Biped dynamics and balance

  • It has been reported that with aging the ability to maintain an upright position decreases and a rate of falling causing serious injuries and even death are quite frequent. With the aging society it is therefore important to understand and isolate the mechanisms that are critical for maintaining balance. Mathematical models of upright standing can be studied to address this question. Some of these models involve the presence of discontinuous nonlinearities and time delays.

    • Continuation for experiments (from Jan Sieber's website, see link to Jan Sieber)

    Dynamics of piecewise-smooth systems with time delay

  • Dynamics of systems with relay feedback, hysteresis and time delay.

    • Link:
  • Colleagues Jan Sieber

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    • Publications

  • Books

    • M. di Bernardo, C. Budd, A. R. Champneys, P. Kowalczyk, Piecewise-smooth Dynamical Systems: Theory and Applications (2008) (see Springer).

     

  • Manuscripts in preparation

    [16] P. Glendinning, P. Kowalczyk, and A. B. Nordmark, Attractors near grazing-sliding bifurcations, To be submitted to Nonlinearity, March 2011

  • Submitted for publication/In revision

    • [15] P. Kowalczyk, P. Glendinning, Martin Brown, Gustavo Medrano-Cerda, Houman Dallali, and Jonathan Shapiro Modelling human balance using switched systems with linear feedback control, In revision: Interdiscpilinary Journal of the Royal Society Interface, March 2011

    [14] P. Kowalczyk, P. Glendinning Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems Submitted for publication to Chaos: An interdisciplinary Journal of Nonlinear Science, March 2011

  • Journal publications

    • [13] P. Glendinning, P. Kowalczyk, Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type, Physica D, 239(1-2), pp.58-71, (2010)

    [12] J. Sieber, P. Kowalczyk, Small-scale instabilities in dynamical systems with sliding, Physica D, 239(1-2), pp. 44-57, (2010)

    [11] P. Glendinning, P. Kowalczyk, Dynamics of a hybrid thermostat model with discrete sampling time control, Dynamical Systems, 24(3), pp. 343-360, (2009)

    [10] 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.629-701, (2008)

    [9] 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. 85-108, (2007)

    [8] P. Kowalczyk, P.T. Piiroinen, Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator, Physica D, 237(8), pp.1053-1073, (2007)

    [7] 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 Time-Delay, Accepted for publication, (2007).

    [6] A. B. Nordmark and P. Kowalczyk, A codimension-two scenario of sliding solutions  in  grazing-sliding bifurcations,, Nonlinearity  19(1) pp. 1-26, (2006) 

    [5] P. Kowalczyk, M. di Bernardo, A. R. Champneys, S.  J. Hogan, M. Homer, Yu. A. Kuznetsov and P. T. Piiroinen, Two-parameter nonsmooth bifurcations of limit cycles: classification and open problems, International Journal of bifurcation and chaos, Vol. 16 No. 3, pp.601-629, (2006)

    [4] P. Kowalczyk and M. di Bernardo, Two-parameter degenerate sliding bifurcations in Filippov systems, Physica D, Vol. 204 pp. 204 - 229, (2005)

    [3] P. Kowalczyk, Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps, Nonlinearity, Vol. 18 pp. 485-504, (2005) 

    [2] M. di Bernardo, P. Kowalczyk,  and A. B. Nordmark,   Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry-friction oscillators, International Journal of Bifurcation and Chaos, Vol. 13, No. 10 pp. 2935-2948, (2003),

    [1] M. di Bernardo, P. Kowalczyk,  and A. B. Nordmark,   Bifurcations of dynamical systems with sliding: derivation of normal-form mappings, Physica D,  volume 170, pp. 175-205, (2002)

  • Conference proceedings

    P. Kowalczyk, J. Sieber, Robustness of grazing-sliding bifurcations in Filippov type systems, To appear in the proceedings of Second IFAC meeting related to analysis and control of chaotic systems, London 2009

    P. Kowalczyk, A. B. Nordmark, Bifurcations in non-smooth models of
    mechanical systems, To appear in the proceeding of EUROMECH 500 conference on Non-smooth 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 Stick-Slip 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))

    J. Sieber, P. Kowalczyk: Event collisions in systems with delayed switches . Proceedings of the 6th IFAC Workshop on Time-Delay Systems, L'Aquila, Italy, 2006

    M. di Bernardo, A.R. Champneys, P. Kowalczyk, Corner-Collision and Grazing-Sliding: practical examples of border-collision 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 Springer-Verlag  (2001), pp. 361-374

    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

    Invited lectures

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