Periodic Solutions of Differential Systems

2020 ◽  
pp. 223-261
Author(s):  
George Dinca ◽  
Jean Mawhin
Keyword(s):  
Periodic Solutions ◽  
Differential Systems

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

scholarly journals Existence for Singular Periodic Problems: A Survey of Recent Results

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Jifeng Chu ◽  
Juntao Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Differential Systems ◽  
Singular Differential Equations ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

scholarly journals Periodic Solutions of a Periodic FitzHugh–Nagumo System

2015 ◽  
Vol 25 (13) ◽  
pp. 1550180 ◽  
Author(s):  
Jaume Llibre ◽  
Claudio Vidal
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Existence Of Periodic Solutions

Recently some interest has appeared for the periodic FitzHugh–Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems.

scholarly journals Periodic Solutions in a Given Set of Differential Systems

2001 ◽  
Vol 264 (2) ◽  
pp. 495-509 ◽  
Author(s):  
Jan Andres ◽  
Bohumil Krajc
Keyword(s):  
Periodic Solutions ◽  
Differential Systems

scholarly journals ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1993 ◽  
Vol 24 (2) ◽  
pp. 173-188
Author(s):  
LIHONG HUANG ◽  
JIANSHE YU
Keyword(s):  
Periodic Solutions ◽  
Special Form ◽  
Differential Systems ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Differential Systems

In this paper three theorems on the existence of nontrivial periodic solutions of the system \[ dx/dt =e(y)\]\[dy/dt =-e(y)f(x)- g(x)\] are proved, which not only generalize some known results on the existence of periodic solutions of Lienard's system (i.e. the special form for $e(y) = y$), but also relax or eliminate some traditional assumptions.

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 Bifurcations from families of periodic solutions in piecewise differential systems

2020 ◽  
Vol 404 ◽  
pp. 132342 ◽  
Author(s):  
Jaume Llibre ◽  
Douglas D. Novaes ◽  
Camila A.B. Rodrigues
Keyword(s):  
Periodic Solutions ◽  
Differential Systems
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