On correct statement of singular BVPs for autonomous systems of nonlinear ODEs with the applications to hydrodynamics

2003 ◽  
Author(s):  
N.B. Konyukhova ◽  
A.I. Sukov
Keyword(s):  
Autonomous Systems ◽  
Nonlinear Odes ◽  
Correct Statement

scholarly journals On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations

2008 ◽  
Vol 465 (2102) ◽  
pp. 585-608 ◽  
Author(s):  
V.K Chandrasekar ◽  
M Senthilvelan ◽  
M Lakshmanan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
First Order ◽  
Open Questions ◽  
Motion Time

Continuing our study on the complete integrability of nonlinear ordinary differential equations (ODEs), in this paper we consider the integrability of a system of coupled first-order nonlinear ODEs of both autonomous and non-autonomous types. For this purpose, we modify the original Prelle–Singer (PS) procedure so as to apply it to both autonomous and non-autonomous systems of coupled first-order ODEs. We briefly explain the method of finding integrals of motion (time-independent as well as time-dependent integrals) for two and three coupled first-order ODEs by extending the PS method. From this we try to answer some of the open questions in the original PS method. We also identify integrable cases for the two-dimensional Lotka–Volterra system and three-dimensional Rössler system as well as other examples including non-autonomous systems in a straightforward way using this procedure. Finally, we develop a linearization procedure for coupled first-order ODEs.

THE CONCEPT OF AUTONOMOUS SYSTEMS IN INDUSTRY 4.0

2019 ◽  
Vol 12 (1) ◽  
pp. 77-87
Author(s):  
György Kovács ◽  
Rabab Benotsmane ◽  
László Dudás
Keyword(s):  
Industry 4.0 ◽  
Intelligent Systems ◽  
Autonomous Systems ◽  
Essential Element ◽  
Industrial Sector ◽  
Life Cycles ◽  
Multi Agent Systems ◽  
New Paradigm ◽  
Intelligent Machines ◽  
Digital Network

Recent tendencies – such as the life-cycles of products are shorter while consumers require more complex and more unique final products – poses many challenges to the production. The industrial sector is going through a paradigm shift. The traditional centrally controlled production processes will be replaced by decentralized control, which is built on the self-regulating ability of intelligent machines, products and workpieces that communicate with each other continuously. This new paradigm known as Industry 4.0. This conception is the introduction of digital network-linked intelligent systems, in which machines and products will communicate to one another in order to establish smart factories in which self-regulating production will be established. In this article, at first the essence, main goals and basic elements of Industry 4.0 conception is described. After it the autonomous systems are introduced which are based on multi agent systems. These systems include the collaborating robots via artificial intelligence which is an essential element of Industry 4.0.

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