Results 211 to 220 of about 17,826 (235)

SHILNIKOV’S SADDLE-NODE BIFURCATION

International Journal of Bifurcation and Chaos, 1996
In 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.
Glendinning, Paul, Sparrow, Colin
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A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN

Stochastics and Dynamics, 2004
In 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, JOHNSON, RUSSELL ALLAN, F. MANTELLINI   +2 more
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Saddle-Node Bifurcations on Fractal Basin Boundaries

Physical Review Letters, 1995
We 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 ...
, Nusse, , Ott, , Yorke
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Critical saddle-node horseshoes: bifurcations and entropy

Nonlinearity, 2003
The paper deals with a one-parameter family \(\mathcal{O}(D)\) of \(C^\infty\)-diffeomorphisms \((f_\mu)_{\mu \in [-1,1]}\) of a compact disk \(D\) of a two-dimensional manifold \(M.\) It is assumed that for \(\mu < 0\) the limit set of \(f_\mu\) in \(D\) is the union of a sink \(S_\mu\) and a hyperbolic saddle set \(\Lambda_\mu\) conjugate to a ...
Díaz, Lorenzo J., Rios, Isabel L.
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Quantum manifestations of saddle-node bifurcations

Chemical Physics Letters, 1995
Abstract 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.
F. Borondo, A.A. Zembekov, R.M. Benito
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Saddle-node bifurcations for hyperbolic sets

Ergodic Theory and Dynamical Systems, 2002
Hyperbolic sets are robust under perturbations: they persist on an open set of the parameter space. In this paper we investigate the boundary of this open set. Generalizing the theory of fixed points we define saddle-node bifurcations for hyperbolic sets K with one-dimensional unstable directions.
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The Saddle-Node Separatrix-Loop Bifurcation

SIAM Journal on Mathematical Analysis, 1987
In the paper vector fields \(x'=f(x)\), \(x\in {\mathbb{R}}^ 2\), having at some point an equilibrium of saddle-node type with a separatrix loop, are studied. Such vector fields fill a codimension two submanifold \(\Sigma\) of an appropriate Banach space. Author gives analytic conditions that determine whether a two-parameter perturbation of \(x'=f(x)\)
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Critical saddle-node bifurcations and Morse–Smale maps

Physica D: Nonlinear Phenomena, 2004
The authors study the saddle-node bifurcation in diffeomorphisms with a critical homoclinic orbit to a saddle point. More precisely, one considers a typical smooth family \(F_{\gamma}\) of diffeomorphisms that undergoes a saddle-node bifurcation at \(\gamma=0\). For \(\gamma0\).
Hunt, Brian R., Young, Todd R.
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Reversible Saddle-Node Separatrix-Loop Bifurcation

We describe the unfolding of a special variant of the codimension-two Saddle-Node Separatrix-Loop (SNSL) bifurcation that occurs in systems with time-reversibility. While the classical SNSL bifurcation can be characterized as the collision of a saddle-node equilibrium with a limit cycle, the reversible variant (R-SNSL) is characterised by as the ...
Burylko, Oleksandr, Wolfrum, Matthias, Yanchuk, Serhiy   +2 more
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