scholarly journals Bifurcation and stability of periodic solutions from a zero eigenvalue

1979 ◽  
Vol 21 (1) ◽  
pp. 2-20
Author(s):  
K. A. Landman
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Double Zero ◽  
Zero Eigenvalue ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Bifurcation And Stability ◽  
Time Periodic

AbstractA study is made of the branching of time periodic solutions of a system of differential equations in R2 in the case of a double zero eigenvalue. It is shown that the solution need not be unique and the period of the solution is large. The stability of these solutions is analysed. Examples are given and generalizations to larger systems are discussed.

Bifurcation and stability of periodic solutions of differential equations with state-dependent delays

2003 ◽  
Vol 14 (1) ◽  
pp. 3-14 ◽  
Author(s):  
D. SCHLEY
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Perturbation Methods ◽  
Population Models ◽  
Delay Function ◽  
State Dependent ◽  
The Stability ◽  
Bifurcation And Stability

We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

Combined Parametrical and Transversal Excitation of a Stretched String in an Elastic Medium

2001 ◽  
Author(s):  
Caswita ◽  
A. H. P. van der Burgh
Keyword(s):  
Periodic Solutions ◽  
Elastic Medium ◽  
Integrodifferential Equation ◽  
Averaging Method ◽  
Telegraph Equation ◽  
Point Boundary ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Two Parameters ◽  
Time Periodic

Abstract In this paper we consider a two-point boundary alue problem for an integrodifferential equation. This equation can be considered as a nonlinearly perturbed telegraph equation including both parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of two modes. The first mode is generated by parametrical excitation and the second one is generated by vertical (transversal) excitation. This interaction of two modes can occur for special combinations of values of two parameters in the equation For the study of time-periodic solutions the averaging method will be used and the stability of the time-periodic solutions will be analyzed in linear approximation.

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