| Title:
|
Dynamic behavior of vector solutions of a class of 2-D neutral differential systems (English) |
| Author:
|
Tripathy, Arun Kumar |
| Author:
|
Sahu, Shibanee |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
139-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work deals with the analysis pertaining some dynamic behavior of vector solutions of first order two-dimensional neutral delay differential systems of the form $$ \frac {{\rm d}}{{\rm d}t} \begin {bmatrix} u(t)+pu(t-\tau )\\ v(t)+pv(t-\tau )\\ \end {bmatrix} = \begin {bmatrix} a & b \\ c & d \\ \end {bmatrix} \begin {bmatrix} u(t-\alpha )\\ v(t-\beta )\\ \end {bmatrix}. $$ The effort has been made to study $$ \frac {{\rm d}}{{\rm d}t} \begin {bmatrix} x(t)-p(t)h_{1}(x(t-\tau ))\\ y(t)-p(t)h_{2}(y(t-\tau )) \end {bmatrix} + \begin {bmatrix} a(t) & b(t)\\ c(t) & d(t) \end {bmatrix} \begin {bmatrix} f_{1}(x(t-\alpha ))\\ f_{2}(y(t-\beta )) \end {bmatrix} =0, $$ where $p,a,b,c,d,h_1,h_2,f_1,f_2 \in C(\mathbb {R},\mathbb {R})$; $\alpha ,\beta ,\tau \in \mathbb {R}^+$. We verify our results with the examples. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
nonlinear system of neutral differential equations |
| Keyword:
|
asymptotically stable |
| Keyword:
|
Banach's fixed point theorem |
| MSC:
|
34A34 |
| MSC:
|
34C10 |
| MSC:
|
34K40 |
| DOI:
|
10.21136/MB.2024.0156-23 |
| . |
| Date available:
|
2025-02-20T16:12:02Z |
| Last updated:
|
2025-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152880 |
| . |
| Reference:
|
[1] Erbe, L. H., Kong, Q., Zhang, B. G.: Oscillation Theory for Functional Differential Equations.Pure and Applied Mathematics, Marcel Dekker 190. Marcel Dekker, New York (1995). Zbl 0821.34067, MR 1309905, 10.1201/9780203744727 |
| Reference:
|
[2] Grigorian, G. A.: Oscillatory criteria for the systems of two first-order linear differential equations.Rocky Mt. J. Math. 47 (2017), 1497-1524. Zbl 1378.34052, MR 3705762, 10.1216/RMJ-2017-47-5-1497 |
| Reference:
|
[3] Györi, I., Ladas, G.: Oscillation Theory of Delay Differential Equations: With Applications.Oxford Mathematical Monographs. Clarendon Press, Oxford (1991). Zbl 0780.34048, MR 1168471, 10.1093/oso/9780198535829.001.0001 |
| Reference:
|
[4] Mihalíková, B.: Asymptotic behaviour of solutions of two-dimensional neutral differential systems.Czech. Math. J. 53 (2003), 735-741. Zbl 1080.34555, MR 2000065, 10.1023/B:CMAJ.0000024515.64004.7c |
| Reference:
|
[5] Naito, M.: Oscillation and nonoscillation for two-dimensional nonlinear systems of ordinary differential equations.Taiwanese J. Math. 27 (2023), 291-319. Zbl 1521.34032, MR 4563521, 10.11650/tjm/221001 |
| Reference:
|
[6] Opluštil, Z.: Oscillation criteria for two-dimensional system of non-linear ordinary differential equations.Electron. J. Qual. Theory Differ. Equ. 2016 (2016), Article ID 52, 17 pages. Zbl 1363.34098, MR 3533262, 10.14232/ejqtde.2016.1.52 |
| . |
