scholarly journals Continuation theorems for periodic perturbations of autonomous systems

1992 ◽  
Vol 329 (1) ◽  
pp. 41-72 ◽  
Author(s):  
Anna Capietto ◽  
Jean Mawhin ◽  
Fabio Zanolin
Author(s):  
O.S. Kostromina

The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit cycle. Its solution is important both for the theory of synchronization of nonlinear oscillations and for the theory of bifurcations of dynamical systems. In the case of commensurability of the natural frequency of the unperturbed system with frequencies of quasi-periodic perturbation, resonance occurs. Averaged systems are derived that make it possible to ascertain the structure of the resonance zone, that is, to describe the behavior of solutions in the neighborhood of individual resonance levels. The study of these systems allows determining possible bifurcations arising when the resonance level deviates from the level of the unperturbed system, which generates a double limit cycle in a perturbed autonomous system. The theoretical results obtained are applied in the study of a two-frequency quasi-periodic perturbed pendulum-type equation and are illustrated by numerical computations.


2019 ◽  
Vol 12 (1) ◽  
pp. 77-87
Author(s):  
György Kovács ◽  
Rabab Benotsmane ◽  
László Dudás

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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