doc. RNDr. Jan Čermák, CSc.

E-mail:   cermak.j@fme.vutbr.cz 
WWW:   http://www.mat.fme.vutbr.cz/home/cermak
Dept.:   Institute of Mathematics
Dept. of Mathematical Analysis
Position:   Head of Department
Room:   A1/1838
Phone:   +420 54114 2535

2071

Education and academic qualification

  • 01.09.1981-05.06.1986, Brno, Study of the branch of mathematical analysis, Faculty of Science, Masaryk University, Brno
  • 01.09.1991-21.03.1996, Brno, External doctoral study, Mathematical Institute of Academy of Science in Prague, the branch mathematical analysis
  • 5.6. 1986: M.S., Faculty of Science, Masaryk University, Brno, the branch mathematical analysis
  • 21.3. 1996: Ph.D., Mathematical Institute, Academy of Sciences of the Czech Republic, Prague, the branch mathematical analysis
  • 28.5. 1999: Associate Professor, Faculty of Mechanical Engineering, Brno University of Technology, the branch mathematics

Career overview

  • 01.09.1986-, , Institute of Mathematics, FME BUT, research worker, assistant professor, associate professor
  • 1986-1990, research worker, Institute of Mathematics, FME BUT
  • 1990-1999, Assistant Professor, Institute of Mathematics, FME BUT
  • since 1999 Associate Professor, Institute of Mathematics, FME BUT

Pedagogic activities

  • BSC study programme: Mathematics I-III, Mathematical Analysis III, Numerical methods, Mathematical Modelling via Differential Equations
  • MSC study programme, study branch Mathematical Engineering: Fundamentals of Optimal Control Theory
  • Ph.D. study programme: Mathematical Methods of Optimal Control
  • Ph.D. Thesis supervised (7 defended), MSC and BSC Thesis supervised
  • 5 textbooks for subjects Mathematics III, Mathematical Analysis III, Line and Surface Integral, Fundamentals of Optimal Control Theory

Scientific activities

  • Delay differential equations
  • Fractional calculus and fractional differential equations
  • Difference and functional equations
  • Dynamic equations on time scales
  • The research is supported by grant projects of the Czech Science Foundation and by other projects

University activities

  • 1993-1996, member of academic senate of FME BUT
  • since 2004, member of PhD study branch council at FME BUT
  •  2000-2007, pedagogical secretary of Institute of Mathematics of FME BUT
  • since 2007, head of Dept. of Mathematical Analysis

Non-University activities

  • since 2010, member of habilitation committees
  • since 2014, member of the editorial board of the international scientific journal Studies of the University of Žilina (Mathematical series)
  • since 2003, member of organizing and scientific committees of international conferences  (ICDEA, Equadiff, CDDEA)
  • since 2003, reviewer of inaugural dissertations and papers for international journals

Prizing by scientific community

  • invited lectures including the cover of all stay expenses at foreign universities, international conferences and workshops (University of Pannonia, Veszprem, 2010, Comenius University in Bratislava, 2012, ICNDDE 2014, Side, WDDDE 2014, Veszprem)

Projects

  • 1. Oscillatory and asymptotic properties of solutions of linear differential equations, the grant project of the Grant Agency of the Academy of Sciences of the Czech Republic no. A109902/1999, 1999-2001.
  • 2. Qualitative properties of solutions of difference equations, the grant project of the Czech Science Foundation no. 201/01/0079, 2001-2003.
  • 3. Limit properties of solutions of differential equations, the grant project of the Grant Agency of the Academy of Sciences of the Czech Republic no. IAA1163401, 2004-2006.
  • 4. Electronic study supports for the teaching of mathematics at FME BUT, development project of FRVS, no. 512/2007.
  • 5. Oscillatory and asymptotic properties of solutions of differential equations, the grant project of the Czech Science Foundation  no. 201/08/0469, 2008-2010.  
  • 6. Simulation modelling of mechatronic systems, the research plan of the Ministry of Education, Youth and Sports of the Czech Republic no. MSM 0021630518, 2005-2011.
  • 7. Qualitative properties of solutions of differential equations and their applications, the grant project of  the Czech Science Foundation no. P201/11/0768, 2011-2015. 
  • 8. Asymptotic theory of ordinary differential equations of integer and non-integer orders and their numerical discretizations, the grant project of the Czech Science Foundation no. 17-03224S, 2017-2019.

Sum of citations (without self-citations) indexed within SCOPUS

180

Sum of citations (without self-citations) indexed within ISI Web of Knowledge

170

Sum of other citations (without self-citations)

10

Supervised courses:

Publications:

  • ČERMÁK, J.; NECHVÁTAL, L.:
    The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system,
    NONLINEAR DYNAMICS, Vol.87, (2017), No.2, pp.939-954, ISSN 1573-269X, Springer
    journal article
  • ČERMÁK, J.; KISELA, T.; HORNÍČEK, J.:
    Stability regions for fractional differential systems with a time delay,
    Communications in Nonlinear Science and Numerical Simulation, Vol.31, (2016), No.1-3, pp.108-123, ISSN 1007-5704, Elsevier Science BV
    journal article
  • ČERMÁK, J.; NECHVÁTAL, L.; GYŐRI, I.:
    On explicit stability conditions for a linear fractional difference system,
    Fractional Calculus and Applied Analysis, Vol.18, (2015), No.3, pp.651-672, ISSN 1311-0454, Walter de Gruyter GmbH, Berlin/Boston
    journal article
  • ČERMÁK, J.; KISELA, T.:
    Introduction to Stability Theory of Linear Fractional Difference Equations,
    Fractional Calculus: Theory, pp.117-162, ISBN 978-1-63463-002-3, (2014)
    book chapter
  • ČERMÁK, J.; KISELA, T.:
    Exact and discretized stability of the Bagley-Torvik equation,
    Journal of Computational and Applied Mathematics, Vol.269, (2014), No.10, pp.53-67, ISSN 0377-0427, Elsevier
    journal article
  • ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L.:
    Stability regions for linear fractional differential systems and their discretizations,
    APPLIED MATHEMATICS AND COMPUTATION, Vol.219, (2013), No.12, pp.7012-7022, ISSN 0096-3003
    journal article
  • ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P.:
    On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations,
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol.18, (2012), No.11, pp.1781-1800, ISSN 1023-6198, Taylor & Francis
    journal article

List of publications at Portal BUT

Abstracts of most important papers:

  • ČERMÁK, J.; KISELA, T.:
    Exact and discretized stability of the Bagley-Torvik equation,
    Journal of Computational and Applied Mathematics, Vol.269, (2014), No.10, pp.53-67, ISSN 0377-0427, Elsevier
    journal article

    The paper discusses stability and asymptotic properties of a two-term linear fractional differential equation involving the Bagley–Torvik equation as the particular case. These properties are analysed for the exact as well as numerical solutions obtained from the Grünwald–Letnikov discretization of the studied differential equation. As the main results, precise descriptions of the exact and discretized stability regions are presented, including the decay rate of the solutions.
  • ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L.:
    Stability regions for linear fractional differential systems and their discretizations,
    APPLIED MATHEMATICS AND COMPUTATION, Vol.219, (2013), No.12, pp.7012-7022, ISSN 0096-3003
    journal article

    This paper concerns with basic stability properties of linear autonomous fractional differential and difference systems involving derivative operators of the Riemann-Liouville type. We derive stability regions for special discretizations of the studied fractional differential systems including a precise description of their asymptotics.
  • ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P.:
    On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations,
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol.18, (2012), No.11, pp.1781-1800, ISSN 1023-6198, Taylor & Francis
    journal article

    This paper discusses two explicit forms of necessary and sufficient conditions for the asymptotic stability of the autonomous four-term linear difference equation. These conditions are derived by use of the Schur–Cohn criterion converted into a more applicable form.
  • ČERMÁK, J.:
    The stability and asymptotic properties of the Theta-methods for the pantograph equation,
    IMA Journal of Numerical Analysis, Vol.31, (2011), No.4, pp.1533-1551, ISSN 0272-4979, Oxford University Press
    journal article

    This paper discusses stability and asymptotic properties of a numerical solution of the nonhomogeneous pantograph equation. The utilized discretizations originate from the Theta-methods considered on uniform as well as quasi-geometric mesh.
  • ČERMÁK, J.; JÁNSKÝ, J.:
    On the asymptotics of the trapezoidal rule for the pantograph equation,
    Mathematics of Computation, Vol.78, (2009), No.268, pp.2107-2126, ISSN 0025-5718, American Mathematical Society
    journal article

    The paper discusses some problems of the numerical discretizations of the pantograph equation with a special emphasize to the trapezoidal rule discretization. The main result formulates conditions under which the numerical solution has the same decay rate as the exact solution.