Time-stepping methods for constructing periodic solutions in maximally monotone set-valued dynamical systems

2014 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
V. Sessa ◽  
F. Vasca ◽  
M. K. Camlibel
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Time Stepping ◽  
Maximally Monotone Set

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

2015 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco Leine
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Balance Method ◽  
Pros And Cons ◽  
Numerical Approaches

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

A Wavelet Based Procedure to Study Vibrations and Stability

1999 ◽  
Author(s):  
S. Pernot ◽  
C. H. Lamarque
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Time Varying ◽  
Differential Systems ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential

Abstract A Wavelet-Galerkin procedure is introduced in order to obtain periodic solutions of multidegrees-of-freedom dynamical systems with periodic time-varying coefficients. The procedure is then used to study the vibrations of parametrically excited mechanical systems. As problems of stability analysis of nonlinear systems are often reduced after linearization to problems involving linear differential systems with time-varying coefficients, we demonstrate the method provides efficient practical computations of Floquet exponents and consequently allows to give estimators for stability/instability levels. A few academic examples illustrate the relevance of the method.

scholarly journals Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms

2016 ◽  
Vol 260 (7) ◽  
pp. 6108-6129 ◽  
Author(s):  
Márcio R.A. Gouveia ◽  
Jaume Llibre ◽  
Douglas D. Novaes ◽  
Claudio Pessoa
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Normal Forms ◽  
Piecewise Smooth

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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