Interaction of two systems with saddle-node bifurcations on invariant circles. I. Foundations and the mutualistic case [PDF]
, 2013 The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system.
Baesens, Claude, MacKay, Robert S.
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Direct transition to high-dimensional chaos through a global bifurcation [PDF]
, 2005 In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step.
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Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
Abstract and Applied Analysis, 2013 The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several ...
Xia Liu, Yepeng Xing
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Abrupt bifurcations in chaotic scattering : view from the anti-integrable limit [PDF]
, 2013 Bleher, Ott and Grebogi found numerically an interesting chaotic phenomenon in 1989 for the scattering of a particle in a plane from a potential field with several peaks of equal height.
Baesens, Claude +2 more
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Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
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Global bifurcations close to symmetry [PDF]
, 2016 Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere.
Labouriau, Isabel S. +1 more
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Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System
Micromachines, 2023 Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes.
Yijun Zhu, Huilin Shang
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Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
, 2012 A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor.
Abad A. +19 more
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Weak chimeras in minimal networks of coupled phase oscillators [PDF]
, 2014 We suggest a definition for a type of chimera state that appears in networks of indistinguishable phase oscillators. Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, we show that this means they cannot ...
Ashwin, Peter, Burylko, Oleksandr
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Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect
Mathematics, 2021 This paper deals with a diffusive predator–prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator–prey model with cooperative hunting and Allee effect.
Yanfei Du, Ben Niu, Junjie Wei
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