Author:
Bácsi Ádám,Kocsis Albert Tihamér
Abstract
AbstractWe study the autonomous systems of quadratic differential equations of the form $${\dot{x}}_i(t)={\textbf{x}}(t)^T {\textbf{A}}_i {\textbf{x}}(t) + {\textbf{v}}_i^T {\textbf{x}}(t)$$
x
˙
i
(
t
)
=
x
(
t
)
T
A
i
x
(
t
)
+
v
i
T
x
(
t
)
with $${\textbf{x}}(t) = (x_1(t),$$
x
(
t
)
=
(
x
1
(
t
)
,
$$x_2(t), \ldots ,x_i(t),\dots )$$
x
2
(
t
)
,
…
,
x
i
(
t
)
,
⋯
)
which, in general, cannot be solved exactly. In the present paper, we introduce a subclass of analytically solvable quadratic systems, whose solution is realized through a multi-dimensional generalization of the inversion which transforms a quadratic system into a linear one. We provide a constructive algorithm which, on one hand, decides whether the system of differential equations is analytically solvable with the inversion transformation and, on the other hand, provides the solution. The presented results apply for arbitrary, finite number of variables.
Funder
Széchenyi István University
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics