Results 151 to 160 of about 3,059 (189)

Flip Bifurcation of a Class of Discrete-time Neural Networks

2009 WRI Global Congress on Intelligent Systems, 2009
In this paper, a class of discrete-time system modeling a network with two neurons is considered. Its flip bifurcations (also called period-doubling bifurcations for map) are demonstrated by deriving the equation describing the flow on the center manifold.
Rong Yu, Xiaoliang Zhou
exaly   +2 more sources

Flip-Flip Bifurcation in a Mathematical Cardiac System

International Journal of Bifurcation and Chaos, 2019
We study the intersection of double-flip (period-doubling) bifurcations in a parameter plane. We derive normal forms for discrete-time and continuous-time systems. Using these normal forms, we clarify the bifurcation structure around the flip-flip bifurcation point. We apply these analytical results to a system of coupled ventricular cell models.
Hiroyuki Kitajima, Toru Yazawa
openaire   +2 more sources

Resonant Homoclinic Flip Bifurcations

Journal of Dynamics and Differential Equations, 2000
Homoclinic bifurcations gained a lot of attention because they are closely related to transitions to chaotic dynamics. Many kinds of homoclinic bifurcations were studied (the best known is the Shil'nikov case of a homoclinic orbit to a saddle-focus equilibrium).
Homburg, A.J., Krauskopf, B.
openaire   +2 more sources

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
openaire   +1 more source

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 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS

Chinese Annals of Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shui, Shuliang, Zhu, Deming
openaire   +2 more sources

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
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source

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 ...
Qi Cheng, Shengfu Deng
openaire   +2 more sources