Results 181 to 190 of about 145,268 (214)

DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

International Journal of Bifurcation and Chaos, 2013
In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic ...
Xingbo Liu, Junying Liu, Deming Zhu
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BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS

International Journal of Bifurcation and Chaos, 2012
In this paper, heteroclinic loop bifurcations with double orbit flips are investigated in four-dimensional vector fields. We obtain the bifurcation equations by setting up a local coordinate system near the rough heteroclinic orbit and establishing the Poincaré map.
Xingbo Liu, Zhenzhen Wang, Deming Zhu
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Codimension-3 Flip Bifurcation of a Class of Difference Equations

International Journal of Bifurcation and Chaos, 2018
In this paper, we consider a one-dimensional difference equation with three parameters, the derivative of which at a fixed point has an eigenvalue [Formula: see text] as the parameters are all zero. In the case that both nondegeneracy conditions of the flip bifurcation and the generalized flip bifurcation are not satisfied, by computing normal form ...
Jiyu Zhong, Xingwang Zhou
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Flip bifurcations of two systems of difference equations

Mathematical Methods in the Applied Sciences, 2020
This paper investigates the bifurcations of the following difference equations where a,b,c, and d are positive constants and the initial conditions x0 and y0 are positive numbers. Psarros, Papaschinopoulos, and Schinas (Math. Methods Appl. Sci., 2016, 39: 5216–5222) presented the semistability of the fixed point (0,0) when one eigenvalue is equal to ...
Shengfu Deng
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NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP

International Journal of Bifurcation and Chaos, 2011
Heteroclinic bifurcations in four-dimensional vector fields are investigated by setting up local coordinates near a heteroclinic loop. This heteroclinic loop consists of two principal heteroclinic orbits, but there is one stable foliation that involves an inclination flip.
Shuliang Shui, Jingjing Li, Xuyang Zhang
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Numerical analysis of the flip bifurcation of maps

Applied Mathematics and Computation, 1991
Discrete dynamical systems depending on a paramter \(\alpha\) are considered: \(x(t+1)=f_{\alpha}(t).\) It is assumed that an \(n\times n\) matrix \(A_{\alpha}\) and a smooth map \(g_{\alpha}\) with \(f_{\alpha}(x)=A_{\alpha}x+g_{\alpha}(x)\) and \(g_{\alpha}(0)=0\), \(\partial g/\partial x|_{\alpha =0}=0\) exists. Problems of this type are of interest
Kuznetsov, Yu. A., Rinaldi, S.
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Flip bifurcation and Neimark–Sacker bifurcation in a discrete predator–prey model with harvesting

International Journal of Biomathematics, 2019
In this paper, a difference-algebraic predator–prey model is proposed, and its complex dynamical behaviors are analyzed. The model is a discrete singular system, which is obtained by using Euler scheme to discretize a differential-algebraic predator–prey model with harvesting that we establish.
Wei Liu, Yaolin Jiang
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Homoclinic flip bifurcations accompanied by transcritical bifurcation

Chinese Annals of Mathematics, Series B, 2011
The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
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Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

Acta Mathematica Sinica, English Series, 2005
The authors consider the general 4-dimensional system in a resonant orbit flip situation. The resonance takes place between the two principal eigenvalues. This is a kind of codimension-3 bifurcation. The authors obtain the existence, number, coexistence of the 1-homoclinic orbit, 1-periodic orbit and 2-homoclinic orbit, etc.
Zhang, Tiansi, Zhu, Deming
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Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions

Acta Mathematica Sinica, English Series, 2006
For higher dimensional systems, bifurcations of a degenerate homoclinic orbit with orbit flip are studied. By establishing local coordinates near the homoclinic orbit, conditions are given sufficient for the existence and uniqueness of a 1-homoclinic orbit and a 1-periodic orbit.
Wu, Ran Chao, Sun, Jian Hua
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