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Bifurcation Structures for MultiModal Maps
"... We discuss the bifurcation structure in multimodal maps and construct explicitly the bifurcation diagrams for short periodic orbits in fewmodal maps using symbolic dynamics. We conjecture this topological picture to be valid for all nmodal maps and perform numerical experiments for polynomial m ..."
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Cited by 1 (1 self)
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maps which agrees with the symbolic dynamics results. In this article we will discuss the structure of bifurcations in the parameter space for nmodal maps of the interval. We want to show that an nmodal map has a universal global bifurcation structure for all periodic and nonperiodic orbits in an n
Quantitative universality for a class of nonlinear Transformations
 J. Statistical Physics
, 1978
"... A large class of recursion relations xn+l = Af(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum 2. With f(2) f(x) ~ Ix 21 " (for Ix 21 su ..."
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Cited by 263 (0 self)
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sufficiently small), z> 1, the universal details depend only upon z. In particular, the local structure of highorder stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio c ~ (a = 2.5029078750957... for z = 2). This structure is determined by a
A New Approach to Measuring Financial Contagion
, 2002
"... contagion captures the coincidence of extreme return shocks across countries within a region the extent of contagion, its economic significance, and its determinants using a multinomial 1990s, we find that contagion, when measured by the coincidence within and across regions of changes, and condit ..."
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Cited by 185 (4 self)
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Reserve Bank of Chicago Annual Conference on Bank Structure and Competition, Global Investment Conference on International Investing (Whistler), and the NYSE Conference on Global Equity Markets in Transition (Hawaii) improved the paper.
Global Bifurcation On Time Scales
 J. MATH. ANAL. APPL
, 2002
"... We consider the structure of the solution set of a nonlinear SturmLiouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, an ..."
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Cited by 4 (1 self)
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We consider the structure of the solution set of a nonlinear SturmLiouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization
The Universal Metric Properties of Nonlinear Transformations
, 1979
"... The role of functional equations to describe the exact local structure of highly bifurcated attractors of x~+l = Af(xn) independent of a specific f is formally developed. A hierarchy of universal functions g~(x) exists, each descriptive of the same local structure but at levels of a cluster of 2 ~ p ..."
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Cited by 128 (0 self)
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The role of functional equations to describe the exact local structure of highly bifurcated attractors of x~+l = Af(xn) independent of a specific f is formally developed. A hierarchy of universal functions g~(x) exists, each descriptive of the same local structure but at levels of a cluster of 2
Bifurcation analysis of chemical reaction mechanisms. II. Hopf bifurcation analysis
 Journal of Chemical Physics
, 1993
"... Oneand twoparameter Hopf bifurcation behavior is analyzed for several variants of the CitriEpstein mechanism of the chloriteiodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifur ..."
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Cited by 3 (0 self)
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in the unfolding, and features such as locally isolated branches of periodic orbits and bistability of a periodic orbit and a steady state are found. Inferences about the global periodic orbit structure and the existence of nearby codimension three Hopf bifurcation points are drawn by piecing together the local
Dewetting Films: Bifurcations and concentrations
 NONLINEARITY
, 2001
"... Under the influence of longrange attractive and shortrange repulsive forces, thin liquid films rupture and form complex dewetting patterns. This paper studies this phenomenon in one space dimension within the framework of fourthorder degenerate parabolic equations of lubrication type. We derive t ..."
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Cited by 25 (10 self)
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the global structure of the bifurcation diagram for steadystate solutions. A stability analysis of the solution branches and numerical simulations suggest coarsening occurs. Furthermore, we study the behaviour of solutions in the limit that shortrange repulsive forces are neglected. Both asymptotic analysis
Ranking on Data Manifolds
 Advances in Neural Information Processing Systems 16
, 2004
"... The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data. ..."
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Cited by 144 (1 self)
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The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data
Scale and the differential structure of images
 Image and Vision Computing
, 1992
"... Why and how one should study a scalespace is prescribed by the universal physical law of scale invariance, expressed by the socalled Pitheorem. The fact that any image is a physical observable with an inner and outer scale bound, necessarily gives rise to a 'scalespace representation', ..."
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Cited by 116 (14 self)
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partirzl derivatives. They enable local image analysis through the detection of local differential structure in a robust wuy, while at the same time capturing global features through the extra scale degree of freedom. In this paper we show why the operations of scaling and differentiation cannot
Results 1  10
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1,790