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SHILNIKOV’S SADDLE-NODE BIFURCATION
International Journal of Bifurcation and Chaos, 1996In 1969, Shilnikov described a bifurcation for families of ordinary differential equations involving n≥2 trajectories bi-asymptotic to a non-hyperbolic stationary point. At nearby parameter values the system has trajectories in correspondence with the full shift on n symbols.
Colin Sparrow, Paul Glendinning
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A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN
Stochastics and Dynamics, 2004In this paper we study certain differential equations depending on a small parameter ε which exhibit a bifurcation of saddle-node type as ε passes through zero. We use a classical averaging technique together with methods and results from the modern theory of nonautonomous differential equations.
FABBRI, ROBERTA +2 more
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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2019
The negative or hyperpolarization pulse stimulation induces action potential, i.e. the post-inhibitory rebound spike, which has been widely observed in various single neurons with hyperpolarization-activated cation current ([Formula: see text]) in ...
Linan Guan, Bin-Bin Jia, Huaguang Gu
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The negative or hyperpolarization pulse stimulation induces action potential, i.e. the post-inhibitory rebound spike, which has been widely observed in various single neurons with hyperpolarization-activated cation current ([Formula: see text]) in ...
Linan Guan, Bin-Bin Jia, Huaguang Gu
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Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1, 1)SN - (A)
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2021Our goal is to make a global study of the class [Formula: see text] of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite and infinite ...
Joan C. Artés +2 more
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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2015
We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend o nt he potential
Jianhua Yang +3 more
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We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend o nt he potential
Jianhua Yang +3 more
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Saddle-node bifurcations in the spectrum of HOCl
The Journal of Chemical Physics, 2000A detailed analysis of the bound-state spectrum of HOCl (hypoclorous acid) in the ground electronic state is presented. Exact quantum mechanical calculations (filter diagonalization) are performed employing an ab initio potential energy surface, which has been constructed using the multireference configuration-interaction method and a quintuple-zeta ...
J. Hauschildt +7 more
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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2016
In this paper, we firstly employ the normal form theory of delayed differential equations according to Faria and Magalhaes to derive the normal form of saddle-node-Hopf bifurcation for the general retarded functional differential equations.
Heping Jiang, Jiao Jiang, Yongli Song
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In this paper, we firstly employ the normal form theory of delayed differential equations according to Faria and Magalhaes to derive the normal form of saddle-node-Hopf bifurcation for the general retarded functional differential equations.
Heping Jiang, Jiao Jiang, Yongli Song
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Quantum manifestations of saddle-node bifurcations
Chemical Physics Letters, 1995Abstract We show that the periodic orbits originating from a saddle-node bifurcation have a profound influence on the topology of the vibrational wavefunctions of the LiNC/LiCN molecular system described by a realistic and complex potential energy surface. The underlying classical structures (manifolds) are examined in detail.
A. A. Zembekov +2 more
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Nonautonomous saddle-Node bifurcation in a Canonical electrostatic MEMS
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2013We study the existence and stability of periodic solutions of a canonical mass-spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) by means of classical topological techniques like a priori bounds, Leray–Schauder degree and ...
Alexander Gutiérrez, P. Torres
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Saddle-Node Bifurcations on Fractal Basin Boundaries
Physical Review Letters, 1995We demonstrate and analyze a bifurcation producing a type of fractal basin boundary which has the strange property that any point that is on the boundary of that basin is also simultaneously on the boundary of at least two other basins. We give rigorous general criteria guaranteeing this phenomenon, present illustrative numerical examples, and discuss ...
Helena E. Nusse +2 more
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