Bifurcation of a periodic solution of a system of ordinary differential equations

1987 ◽  
Vol 38 (3) ◽  
pp. 339-342
Author(s):  
M. T. Terekhin
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations

Smoothness of Asymptotic Phase Revisited

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Flaviano Battelli ◽  
Kenneth J. Palmer
Keyword(s):  
Periodic Solution ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stable Manifold ◽  
Autonomous System ◽  
Asymptotic Phase

AbstractIt is well-known that solutions on the stable manifold of a hyperbolic periodic solution of an autonomous system of ordinary differential equations have an asymptotic phase which has the same order of smoothness as the vector field. In this paper we show if the system depends on a parameter that, in general, the asymptotic phase loses one order of smoothness in the parameter.

scholarly journals On the existence of periodic solution of some quasilinear differential equations with impulses

2004 ◽  
Vol 26 (1) ◽  
pp. 55-64
Author(s):  
Le Luong Tai
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Equation System ◽  
Existence Of Periodic Solutions

As for ordinary differential equations, one of the problems that especially attract the attention of many mathematicians is the problem on the existence of periodic solutions of the differential equation systems with impulses. In this paper, we study the periodic solutions of the equation system under of the form...

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