Periodic solutions of asymptotically linear dynamical systems

1994 ◽  
Vol 1 (3) ◽  
pp. 267-280 ◽  
Author(s):  
Vieri Benci ◽  
Donato Fortunato
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Asymptotically Linear ◽  
Linear Dynamical Systems

scholarly journals SELF-OSCILLATIONS AND SLIDING IN RELAY FEEDBACK SYSTEMS: SYMMETRY AND BIFURCATIONS

2001 ◽  
Vol 11 (04) ◽  
pp. 1121-1140 ◽  
Author(s):  
MARIO DI BERNARDO ◽  
KARL HENRIK JOHANSSON ◽  
FRANCESCO VASCA
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Bifurcation Analysis ◽  
Feedback System ◽  
Feedback Systems ◽  
Relay Feedback ◽  
Linear Dynamical Systems ◽  
Local Bifurcations

This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.

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