scholarly journals The Research of Periodic Solutions of Time-Varying Differential Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Wenjun Liu ◽  
Yingxin Pan ◽  
Zhengxin Zhou
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Riccati Equations ◽  
Linear Differential System ◽  
Time Varying ◽  
Linear Differential

We have studied the periodicity of solutions of some nonlinear time-varying differential models by using the theory of reflecting functions. We have established a new relationship between the linear differential system and the Riccati equations and applied the obtained results to discuss the behavior of periodic solutions of the Riccati equations.

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 On a linear differential system of neutral type

1986 ◽  
Vol 40 (2) ◽  
pp. 226-233
Author(s):  
P. Ch. Tsamatos
Keyword(s):  
Fixed Points ◽  
Differential System ◽  
Finite Dimension ◽  
Neutral Type ◽  
Common Fixed Points ◽  
Linear Differential System ◽  
Linear Differential

AbstractThis paper is concerned with the neutral type differential system with derivating arguments. By decomposing the space of initial functions into classes, it is derived that, for each class, the space of corresponding solutions is of finite dimension. The case of common fixed points of the arguments is also studied.

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