The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations

2016 ◽  
Vol 40 (8) ◽  
pp. 2834-2846
Author(s):  
Changrong Zhu ◽  
Bin Long
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Homoclinic Orbit

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.

PERIODIC SOLUTIONS FOR A FOURTH-ORDER EQUATION AND APPLICATIONS IN A MODEL OF STRUCTURAL MECHANICS

2004 ◽  
Vol 14 (04) ◽  
pp. 1477-1488
Author(s):  
XIAOLI HU ◽  
JIBIN LI
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Homoclinic Orbit ◽  
Order Equation ◽  
Shooting Methods ◽  
Fourth Order Equation ◽  
Elastic Foundations

By developing topological shooting methods, the existence of single-humped periodic solutions and homoclinic orbit for a class of fourth-order ordinary differential equations is obtained, under some general conditions. Using these strict mathematical conclusions to a model of the deflection patterns of elastic struts resting on elastic foundations, the existence of single-humped periodic solutions which have been found by asymptotical and numerical methods is determined. An estimation of the half-period of the periodic solutions is also given.

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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