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Proceedings of the American Mathematical Society, 1964 A description of the classical bifurcation problem will be found in Minorsky [1, Chapter V] and Andronov and Chaikin [2, Chapter 6]. Here the functions fi and f2 are required to be analytic and the proof depends on the series expansion guaranteed by the analyticity. In [3, Chapter IV, ?6], K. 0.
Paul Waltman
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Bifurcations of transition states: Morse bifurcations [PDF]
Nonlinearity, 2014 A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy-level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy-level into two components and has no local recrossings.
Robert S. MacKay, Dayal C. Strub
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Bifurcation and criticality [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2019 Equilibrium and nonequilibrium systems exhibit power-law singularities close to their critical and bifurcation points respectively. A recent study has shown that biochemical nonequilibrium models with positive feedback belong to the universality class of the mean-field Ising model.
Sayantari Ghosh, Indrani Bose
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The Pitchfork Bifurcation [PDF]
International Journal of Bifurcation and Chaos, 2017 We present the development of a new theory of the pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.
Indika Rajapakse, Steve Smale
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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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Bifurcation of homoclinics [PDF]
Proceedings of the American Mathematical Society, 2007 We show that homoclinic trajectories of nonautonomous vector fields parametrized by a circle bifurcate from the stationary solution when the asymptotic stable bundles of the linearization at plus and minus infinity are “twisted” in different ways.
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Bifurcation of Hyperbolic Planforms [PDF]
Journal of Nonlinear Science, 2011 Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space.
Chossat, Pascal +2 more
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Traveling waves in a parabolic problem with a rotation on the circle [PDF]
Компьютерные исследования и моделирование, 2017 Optical systems with two-dimensional feedback demonstrate wide possibilities for studying the nucleation and development processes of dissipative structures.
Yuliya Aleksandrovna Khazova
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IEEE Transactions on Automatic Control, 2004 The article of record as published may be located at http://dx.doi.org/10.1109/TAC.2004.832199 A parametrized nonlinear differential equation can have multiple equilibria as the parameter is varied. A local bifurcation of a parametrized differential equation occurs at an equilibrium where there is a change in the topological character of the nearby ...
Krener, Arthur J. +2 more
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Study on the Compatibility of Multi-Bifurcations by Simulations of Pattern Formation
IEEE Access, 2019 Bifurcation is considered the main mathematical mechanism for the formation of spatial self-organizing patterns in many studies. When bifurcation was initially defined, only the transition of the system from stable state to unstable state or from uniform
Feifan Zhang +4 more
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