Research papers

[18] I. Balázs, Á. Garab
Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay, submitted. preprint link

[17] F. A. Bartha, Á. Garab, T. Krisztin
Morse decomposition for state-dependent delay differential equations,  J. Dynam. Differential Equations, published online, 2025. link pdf

[16] G. Sayyar, Á. Garab, G. Röst
Evolution into chaos – implications of the trade-off between transmissibility and immune evasion, Infectious Disease Modelling, 10(2025), No. 3, 909-923. link

[15] V. Benekas, Á. Garab, A. Kashkynbayev, I.P. Stavroulakis
Oscillation criteria for linear difference equations with several variable delays, Opuscula Math. 41(2021), No. 5, 613-627. link pdf


[14] Á. Garab, M. Pituk
Convergence in nonautonomous linear differential equations with Kirchhoff coefficients, Systems Control Lett. 149(2021), 104884. link pdf


[13] Á. Garab, C. Pötzsche, M. Pituk
Linearized stability in the context of an example by Rodrigues and Solŕ-Morales, J. Differential Equations, 269(2020), No. 11, 9838-9845. link pdf

[12] Á. Garab, I.P. Stavroulakis
Oscillation criteria for first order linear delay differential equations with several variable delays, Appl. Math. Lett. 106, August 2020, 106366.  link pdf

[11] Á. Garab
Absence of small solutions and existence of Morse decomposition for a cyclic system of delay differential equations, J. Differential Equations 269(2020), No. 6, 5463-5490.  link pdf (preprint)

[10] Á. Garab
A sharp oscillation criterion for a linear differential equation with variable delay, Symmetry 11(2019), No. 11, Article No. 1332.  link pdf 

[9] Á. Garab, M. Pituk, I.P. Stavroulakis
A sharp oscillation criterion for linear delay differential equations, Appl. Math. Lett. 93, July 2019, 58-65. link pdf (preprint) 

[8] Á. Garab, V. Jiménez López, E. Liz
Global asymptotic stability of a generalization of the Pielou difference equation, Mediterr. J. Math. 16(2019), No. 4, 16:93. link pdf (preprint)

[7] Á. Garab, C. Pötzsche
Morse decomposition for delay-difference equations,  J. Dynam. Differential Equations 31(2019), No. 2,  903-932. link pdf

[6] Á. Garab
A note on dissipativity and permanence of delay difference equations, Electron. J. Qual. Theory Differ. Equ. 2018, No. 51, 1-12. link pdf

[5] Á. Garab, V. Kovács, T. Krisztin
Global stability of a price model with multiple delays, Discrete Contin. Dyn. Syst. 36(2016), No. 12, 6855–6871. link pdf (un-refereed author version)

[4] F.A. Bartha, Á. Garab
Necessary and sufficient condition for the global stability of a delayed discrete-time single neuron model, J. Comput. Dyn. 1(2014), No. 2, 213-232. link  pdf (preprint)

[3] F.A. Bartha, Á. Garab, T. Krisztin
Local stability implies global stability for the 2-dimensional Ricker map, J. Difference Equ. Appl. 19(2013), No. 12, 2043-2078. link pdf (preprint) (Recognized as the best paper of the year 2013 in J. Difference Equ. Appl.)

[2] Á. Garab
Unique periodic orbits of a delay differential equation with piecewise linear feedback function, Discrete Contin. Dyn. Syst. 33(2013), No. 6, 2369-2387. link pdf (preprint)

[1] Á. Garab, T. Krisztin
The period function of a delay differential equation and an application, Period. Math. Hungar. 63(2011), No. 2, 173-190, 2011. link pdf (preprint)



PhD thesis

Á. Garab, Biológiai jelenségeket modellező késleltetett differenciál- és differenciaegyenletek vizsgálata (in Hungarian) [Delayed differential and difference equations modeling biological phenomena], 2014. Supervisor: Prof. Tibor Krisztin

Outline of the thesis (in English)        Tézisfüzet (in Hungarian)        Full pdf (in Hungarian)

"Science to public" papers

[1]  Á. Garab, Matematikai bizonyítások számítógépek segítségével (in Hungarian) [Computer aided mathematical proofs]. pdf (preprint)

Conference talks

2022    Minisymposium on Qualitative Theory for Linear Hamiltonian Systems and Nonautonomous Dynamical Systems (invited speaker), Equadiff 15, Brno, Czech Republic

2022    Advanced, delayed and mixed equations. Representation of solutions, boundedness, stability (invited speaker), Equadiff 15, Brno, Czech Republic

2020    ICMC Summer Meeting on Differential Equations, 2020 Chapter, Saő Carlos, Brazil.

2019    Difference Equations minisymposium on the conference Dynamics, Equations and Applications (invited speaker), Krakow, Poland.

2019    Minisymposium on Discrete Dynamical Systems and Applications (invited speaker), ICIAM 2019, Valencia, Spain.

2019    11th Colloquium on the Qualitative Theory of Differential Equations, Szeged, Hungary.
 
2018    Veszprém Conference on Differential and Difference Equations and Applications (invited speaker), Veszprém, Hungary.

2018    Szeged Dynamics Days On the Occasion of the 75th Birthday of Professor László Hatvani (poster), Szeged, Hungary.

2018    The Third International Conference on the Dynamics of Differential Equations (poster), Hiroshima, Japan.

2017    East Alpine Meeting on Differential Equations and Dynamical Systems (invited speaker), Vipava, Slovenia.

2017    19th ÖMG Congress and Annual DMV Meeting (invited speaker in the thematic section on Ordinary Differential Equations and Dynamical Systems), Salzburg, Austria.

2017    23rd International Conference on Difference Equations and Applications (ICDEA 2017), Timișoara, Romania.

2017    XXXVII Dynamics Days Europe International Conference, Szeged, Hungary.

2015    Differential equations with variable delay (poster), Toronto, Canada.

2014   AIMS Conference on Dynamical Systems, Differential Equations and Applications, Minisymposium on Discrete Dynamics and Applications (invited speaker), Madrid, Spain.

2014    8th Workshop Structural Dynamical Systems: Computational Aspects - SDS2014 (poster), Bari, Italy.

2014    Szeged Dynamics Days (poster), Szeged, Hungary.

2013    International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary.

2013    1st International Conference on Dynamics of Differential Equations, Atlanta, Georgia, USA.

2012    6th European Congress of Mathematics, Mini-Symposium and Satellite Thematic Session (invited speaker), Krakow, Poland.

2012    The Second Conference of PhD Students in Mathematics, Szeged, Hungary.

2012    Szeged-Timisoara Workshop on Differential Equations, Szeged, Hungary.

2011    Equadiff, Loughborough, England.

2011    9th Colloquium on the Qualitative Theory of Differential Equations, Szeged, Hungary.

2010    The First Conference of PhD Students in Mathematics, Szeged, Hungary.

2009    Equadiff 12, Brno, Czech Republic.



Master thesis (in Hungarian)

2008    Á. Garab, Egy neuronhálózat dinamikai elemzése [Dynamics of a neural network model], témavezető [advisor]: Dr. Krisztin Tibor pdf