Delay differential equations

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Details of project

Identifier

129322

Type

Principal investigator

Krisztin, Tibor

Title in Hungarian

Differenciálegyenletek időkésleltetéssel

Title in English

Delay differential equations

Keywords in Hungarian

időkésleltetés, attraktor, periodikus pálya, összekötő pálya, homoklinikus pálya, hiperbolicitás, stabilitás, állapotfüggő késleltetés

Keywords in English

time delay, attractor, periodic orbit, connecting orbit, homoclinic orbit, hyperbolicity, stability, state-dependent delay

Discipline

Mathematics (Council of Physical Sciences)	100 %
Ortelius classification: Differential equations

Panel

Mathematics and Computing Science

Department or equivalent

Bolyai Institute (University of Szeged)

Participants

Balázs, István
Benedek, Gábor István
Dudás, János
Pham, Ngoc
Van Leeuwen-Polner, Mónika
Vas, Gabriella Ágnes

Starting date

2018-09-01

Closing date

2024-03-31

Funding (in million HUF)

13.622

FTE (full time equivalent)

16.74

state

running project

Final report

Results in Hungarian

Időkésleltetéses differenciálegyenleteket vizsgáltunk. Ezek az egyenletek végtelen dimenziós dinamikai rendszereket definiálnak. Elméleti kutatásaink fontos egyenlettípusokra dolgoztak ki új módszereket. A főbb eredmények: • A nevezetes Mackey-Glass egyenlet egy új megközelítéssel vizsgáltuk. Bonyolult szerkezetű, de stabil periodikus pályák létezését igazoltuk. Ősszekötő és speciálisan homoklinikus pályák létezése van publikálás alatt. • Neuronhálózatokat modellező absztrakt egyenleteket vizsgáltunk a funkcionálanalízis eszközeivel. Karakterizáltuk a linearizált egyenlet spektrumát. Alkalmazásként Hopf bifurkációt bizonyítottunk, és kiszámoltuk a Ljapunov együtthatót. • Állapotfüggű késleltetésű egyenletek új típusaira vezettünk be alkalmas fázistereket, igazoltuk periodikus pályák létezését, leírtuk a megoldás sokaság geometriai tulajdonságait. • Járványterjedési modelleket vizsgáltunk. 18 folyóiratcikket publikáltunk. A Scimago journal ranking szerint 17 cikk Q1 besorolású, ebből 6 D1 besorolású folyóiratban jelent meg. További 5 előkészületben lévő dolgozatot fogunk még publikálásra benyújtani feltüntetve a projekt támogatását.

Results in English

We studied delay differential equations. These equations define infinite-dimensional dynamical systems. In our theoretical investigations, we developed new methods for important classes of delay differential equations. The main results: • We studied the famous Mackey-Glass type equations by introducing a new approach. Stable periodic orbits with complicated structures were obtained. The existence of connecting and in particular, homoclinic orbits is under publication. • Delayed neural field models were investigated as a dynamical system in an appropriate functional analytic setting. The spectrum of the linearized equation was characterized. As an application, Hopf bifurcation was shown, and we computed the Lyapunov coefficient. • We considered different models for epidemic spread. We published 18 research papers. According to the Scimago journal ranking, 17appeared in Q1-ranked journals, and 6 in D1-ranked journals. An additional 5 papers are under preparation with the support of this project.

Full text

https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=129322

Decision

Yes

List of publications

Opoku-Sarkodie, Richmond; Bartha, Ferenc A.; Polner, Mónika; Röst, Gergely: Dynamics of an SIRWS model with waning of immunity and varying immune boosting period, J. Biol. Dyn. 16 (2022), no. 1, 596–618., 2022

Opoku-Sarkodie, R.; Bartha, F. A.; Polner, M.; Röst, G.: Bifurcation analysis of waning-boosting epidemiological models with repeat infections and varying immunity periods, Math. Comput. Simulation 218 (2024), 624–643., 2024

Spek, Len; van Gils, Stephan A.; Kuznetsov, Yuri A.; Polner, Mónika: Hopf bifurcations of two population neural fields on the sphere with diffusion and distributed delays, SIAM J. Appl. Dyn. Syst. 23 (2024), no. 3, 1909–1945., 2024

Gábor Benedek, Tibor Krisztin, Robert Szczelina: Stable Periodic Orbits for Delay Differential Equations with Unimodal Feedback, Journal of Dynamics and Differential Equations, 10 December 2024, online, 2024

Ferenc A. Bartha, Ábel Garab, Tibor Krisztin: Morse Decomposition of Scalar Differential Equations with State-Dependent Delay, Journal of Dynamics and Differential Equations. Published: 27 February 2025, online, 2025

Bartha, Ferenc A.; Krisztin, Tibor; Vígh, Alexandra,: Stable periodic orbits for the Mackey–Glass equation., J. Differential Equations 296 (2021), 15–49., 2021

I. Balázs, P. Getto, G. Röst: A continuous semiflow on a space of Lipschitz functions for adifferential equation with state-dependent delay from cell biology, J. Differential Equations, accepted, 2021

Spek, L.; Dijkstra, K.; van Gils, S.A.; Polner, M.: Dynamics of delayed neural field models in two-dimensional spatial domains, Journal of Differential Equations 317 (2022), 439-473., 2022

Opoku-Sarkodie, R.; Bartha, F.A.; Polner, M.; Röst, G.: Dynamics of an SIRWS model with waning of immunity and varying immune boosting period, Journal of Biological Dynamics 16 (2022), 596-618., 2022

Tibor Krisztin, Hans-Otto Walther: Solution manifolds of differential systems with discrete state-dependent delays are almost graphs, Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 2973–2984., 2023

István Balázs, Tibor Krisztin: Global stability for price models with delay, J. Dyn. Diff. Equat. 31 (2019) 1327–1339., 2019

István Balázs, Tibor Krisztin: A Differential equation with a state-dependent queueing delay, benyújtva, 2019

Szandra Beretka, Gabriella Vas: Saddle-node bifurcation of periodic orbits for a delay differential equation, benyújtva, 2019

Szandra Beretka, Gabriella Vas: Stable periodic solutions for Nazarenko's equation, benyújtva, 2019

István Balázs, Tibor Krisztin: A differential equation with a state-dependent queueing delay, SIAM J. Math. Anal. 52-4 (2020), pp. 3697-3737, 2020

Szandra Beretka, Gabriella Vas: Saddle-node bifurcation of periodic orbits for a delay differential equation, J. Differential Equations 269 (2020), no. 5, 4215–4252., 2020

Szandra Beretka, Gabriella Vas: Stable periodic solutions for Nazarenko's equation, Communications on Pure & Applied Analysis 19 (2020), no. 6, 3257–3281., 2020

István Balázs, Gergely Röst: Hopf bifurcation for Wright-type delay differential equations: The simplest formula, period estimates, and the absence of folds, Communications in Nonlinear Science and Numerical Simulation, Volume 84, 105188 (2020), 2020

Muqbel, Khalil; Vas, Gabriella; Röst, Gergely: Periodic orbits and global stability for a discontinuous SIR model with delayed control, Qual. Theory Dyn. Syst. 19 (2020), no. 2, Paper No. 59, 27 pp., 2020

K. Dijkstra, M. Polner, L. Spek, S. A. van Gils: Dynamics of delayed neural field models in two-dimensional spatial domains, submitted, 2020

J. Dudás, T. Krisztin,: Global stability for the 3-dimensional logistic map, submitted, 2020

I. Balázs, P. Getto, G. Röst: A continuous semiflow on a space of Lipschitz functions for a differential equation with state-dependent delay from cell biology, submitted, 2020

I. Balázs, G. Röst: Hopf bifurcations in Nicholson's blowfly equation are always supercritical., submitted, 2020

J. Dudás, T. Krisztin,: Global stability for the 3-dimensional logistic map, Nonlinearity 34 (2021), no. 2, 894–938., 2021

Krisztin, Tibor: Periodic solutions with long period for the Mackey–Glass equation, Electron. J. Qual. Theory Differ. Equ. 2020, Paper No. 83, 12 pp., 2021

I. Balázs, G. Röst: Hopf bifurcations in Nicholson's blowfly equation are always supercritical., International Journal of Bifurcation and Chaos, 31(05), 2150071 (2021), 2021

Balázs István, Krisztin Tibor: A Differential Equation with a State-Dependent Queueing Delay, SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52: (4) pp. 3697-3737., 2020

Events of the project

2022-05-10 14:12:15

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