Dynamic behavior of vector solutions of a class of 2-D neutral differential systems

Tripathy, Arun Kumar, and Sahu, Shibanee. "Dynamic behavior of vector solutions of a class of 2-D neutral differential systems." Mathematica Bohemica (2025): 139-159. <http://eudml.org/doc/299896>.

@article{Tripathy2025,
abstract = {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.},
author = {Tripathy, Arun Kumar, Sahu, Shibanee},
journal = {Mathematica Bohemica},
language = {eng},
number = {1},
pages = {139-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dynamic behavior of vector solutions of a class of 2-D neutral differential systems},
url = {http://eudml.org/doc/299896},
year = {2025},
}

TY - JOUR
AU - Tripathy, Arun Kumar
AU - Sahu, Shibanee
TI - Dynamic behavior of vector solutions of a class of 2-D neutral differential systems
JO - Mathematica Bohemica
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 139
EP - 159
AB - 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.
LA - eng
UR - http://eudml.org/doc/299896
ER -