scholarly journals Zero-Hopf Bifurcation in a Generalized Genesio Differential Equation

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 354
Author(s):  
Zouhair Diab ◽  
Juan L. G. Guirao ◽  
Juan A. Vera
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Differential System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Periodic Trajectories ◽  
First Order ◽  
Three Dimensional Space

The purpose of the present paper is to study the presence of bifurcations of zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such differential equation in a first-order differential system in the three-dimensional space R3, we are able to prove the existence of a zero-Hopf bifurcation from which periodic trajectories appear close to the equilibrium point located at the origin when the parameters a and c are zero and b is positive.

A first-order volume of fluid convection model in three-dimensional space

2001 ◽  
Vol 36 (2) ◽  
pp. 185-204 ◽  
Author(s):  
Seong-O. Kim ◽  
Yoonsub Sim ◽  
Eui-Kwang Kim
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Volume Of Fluid ◽  
First Order ◽  
Fluid Convection ◽  
Convection Model ◽  
Three Dimensional Space

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals PERIODIC ORBITS NEAR EQUILIBRIA VIA AVERAGING THEORY OF SECOND ORDER

2012 ◽  
Vol 17 (5) ◽  
pp. 715-731
Author(s):  
Luis Barreira ◽  
Jaume Llibre ◽  
Claudia Valls
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Periodic Orbits ◽  
Differential System ◽  
Sufficient Conditions ◽  
First Integral ◽  
Second Order ◽  
Averaging Theory ◽  
First Order

Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of the second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of degenerated Hopf bifurcation.

Straightforward derivation of Hubral’s wavefront curvature differential equation in inhomogeneous isotropic media

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 964-967 ◽  
Author(s):  
Theodor Krey
Keyword(s):  
Differential Equation ◽  
Arbitrary Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
Isotropic Media ◽  
Three Dimensional Space

“Wavefront curvatures in three‐dimensional laterally inhomogeneous media with curved interfaces” (Hubral, 1980, this issue) shows a differential equation [formula (4.1)] which describes the alteration of the wavefront curvature matrix along a raypath in the case of an isotropic velocity v which is an arbitrary function of the locus in the three‐dimensional space. Hubral derives his equation by referring to papers of Popov and Pšenčik (1976, 1978) and Hubral (1979).

XVIII.—The Equation of Conduction of Heat

1926 ◽  
Vol 45 (3) ◽  
pp. 230-244 ◽  
Author(s):  
Marion C. Gray
Keyword(s):  
Differential Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Infinite Cylinder ◽  
Image Position ◽  
Three Dimensional Space

The differential equation of the conduction of heat in ordinary three-dimensional space is generally written in the formwhere v denotes the temperature of the medium at time t. For a medium in which the temperature varies only in one direction, e.g. an infinite cylinder with the temperature varying along the axis, the equation is

Boundary value problems for a model system of first-order equations in three-dimensional space

2015 ◽  
Vol 51 (5) ◽  
pp. 645-651 ◽  
Author(s):  
Bato B. Oshorov ◽  
Bator B. Oshorov
Keyword(s):  
Boundary Value Problems ◽  
Dimensional Space ◽  
Boundary Value ◽  
Three Dimensional ◽  
Model System ◽  
First Order ◽  
Three Dimensional Space
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