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Flip bifurcation and Neimark–Sacker bifurcation in a discrete predator–prey model with harvesting
International Journal of Biomathematics, 2019In 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, 2011The 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, 2005The 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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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip
Nonlinear Dynamics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Yancong, Zhu, Deming
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Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
Acta Mathematica Sinica, English Series, 2006For 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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Bifurcation analysis of the multiple flips homoclinic orbit
Chinese Annals of Mathematics, Series B, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Tiansi, Zhu, Deming
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Degenerate bifurcations of heterodimensional cycle with orbit flip and inclination flip
SCIENTIA SINICA Mathematica, 2013We study the heterodimensional cycle with orbit flip and inclination flip in four-dimensional system. By setting up a new local coordinate system in small tubular neighborhood of unperturbed heterodimensional cycle, we construct a Poincare return map and further obtain the bifurcation equations.
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Heterodimensional cycle bifurcation with two orbit flips
Nonlinear Dynamics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xingbo, Xu, Yancong, Wang, Sisi
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An equivariant, inclination-flip, heteroclinic bifurcation
Nonlinearity, 1996Summary: We examine a heteroclinic bifurcation occurring in families of equivariant vector fields. Within these families, the flows contain structurally stable heteroclinic cycles. The flow can twist around the cycle to produce what is the equivalent of an `inclination-flip' homoclinic orbit.
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Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations.
Suraj Dange +5 more
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