The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenom…
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48 results for “bifurcating behavior”
Study the geometry of bifurcation sets for specific types of functions.
problem Understanding the structure of bifurcation sets for specific types of functions.
method Using blow-ups and parametrization, investigate the Gaussian curvature, principal curvatures, and curve behavior.
result Bifurcation sets of -functions can be parametrized as surfaces in .
The paper studies bifurcations in Lagrangian systems and geodesics.
problem Investigating bifurcations in Lagrangian systems with various boundary conditions.
method Using Morse theory and nullity techniques, the paper establishes conditions for bifurcation in three configurations.
result Unified Morse-theoretic framework connecting geometric focal structure and analytic bifurcation behavior.
Deep learning detects bifurcations in dynamical systems.
problem Predicting catastrophic changes in dynamical systems across sciences.
method Data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries.
result Extracts topologically invariant features to detect bifurcation boundaries in unseen systems.
Study finds many nonplanar minimal spheres in elongated ellipsoids.
problem Existence of nonplanar minimal spheres in elongated ellipsoids.
method Global bifurcation techniques to establish existence and quantify number.
result Arbitrarily many nonplanar minimal spheres exist in elongated ellipsoids.
Study on bifurcations in Lagrangian systems and geodesics on manifolds.
problem Investigating bifurcations in Lagrangian systems and geodesics on Finsler and Riemannian manifolds.
method Employing Morse index and nullity techniques, and refining the Gauss lemma.
result Derivation of precise conditions for bifurcations in geodesic flows.
Predicting unobserved bifurcations in time series with unsupervised parameter extraction.
problem Predicting system behavior with unknown parameters from time series data.
method Reservoir computing framework for unsupervised extraction of slowly varying system parameters.
result Model predicts unknown bifurcations not present in training data.
Topological method detects Hopf bifurcations from time series.
problem Detecting Hopf bifurcations in nonlinear systems from time series data.
method Persistent homology applied to Takens embedding for phase space reconstructions.
result A simple scalar topological functional identifies critical bifurcation points.
Local Neural Operators enable efficient system-level analysis of complex PDEs.
problem System-level analysis of large-scale dynamical systems using neural operators.
method Integrating local Neural Operators with Krylov subspace iterative methods for stability and bifurcation analysis.
result Demonstrated effectiveness of local Neural Operators in fixed-point, stability, and bifurcation analysis of nonlinear PDEs.
Modeling bank leverage dynamics to understand systemic risk in financial markets.
problem Understanding systemic risk in financial markets triggered by bank leverage dynamics.
method Developed a dynamical model of bank leverage, analyzing coupled dynamics in isolated and interconnected bank models.
result Identified a procyclical feedback loop between asset prices and leverage, leading to chaotic dynamics.
This is the second part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, I_F. (See math.DG/0111313 for part I). Having constructed I_F and outlined a proof of its invariance based on bifurcation analysis in part I, in this part we prove a series of gluing theorems to confirm the b…
A simple function shows how neural nets can converge despite high sharpness.
problem Understanding why neural nets converge with high sharpness.
method Constructed a minimal example function and analyzed its training dynamics rigorously.
result Final converging point has sharpness close to .
Study long-term behavior of semi-Markov modulated processes using integral functions.
problem Analyzing long-term behavior of semi-Markov modulated processes involving integral functions.
method Using ergodic semi-Markovian environment and affine stochastic recurrence equation.
result Mixture type laws emerge in long-term limit for processes.
The paper extends curve deformation methods in Minkowski plane.
problem Studying deformations of curves in the Minkowski plane considering their geometry and singularities.
method Extends methods from [17, 18] to analyze 2-parameter families of curves in Minkowski plane.
result Obtains geometry of deformed curves, including inflections, vertices, and lightlike points.
We characterize stationary solutions to McKean-Vlasov equations on the circle.
problem Stationary solutions of McKean-Vlasov equations on the circle.
method Exact equivalence to an infinite-dimensional quadratic system of equations over Fourier coefficients, leading to explicit characterization of stationary states.
result Analytic expressions for the emergence, form, and shape of bifurcations involving multiple Fourier modes, and connections with discontinuous phase transitions.
Toral CW complexes and bifurcation control in Eulerian flows with multiple Hopf singularitiesmath.DS
Study controls bifurcations in Eulerian flows with multiple Hopf singularities.
problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.
method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.
result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.
Study how invariants change under bifurcations of curves.
problem Understanding how invariants of curves change under bifurcations.
method Analyzing , , , and invariants of curves under -bifurcations.
result Invariant changes under bifurcations, preserving its essential properties.
MATLAB toolbox pde2path solves geometric PDEs and finds bifurcations in immersed surfaces.
problem Finding bifurcations in geometric PDEs of immersed surfaces.
method Solving PDEs for surface displacement, updating surface, detecting and localizing bifurcations, and switching branches.
result Symmetry breaking bifurcations in various geometric surfaces.
Study finds bifurcation and local rigidity points for solutions to the Yamabe problem on Aloff-Wallach Spaces.
problem Yamabe problem on Aloff-Wallach Spaces
method Constructing 1-parameter families of solutions and examining changes in the Morse index as the parameter varies.
result Identifies bifurcation and local rigidity points for homogeneous solutions to the Yamabe problem.
The paper studies bifurcations in discrete dynamical systems on manifolds.
problem Understanding bifurcations in discrete dynamical systems on manifolds.
method Topological techniques based on concentricity of manifolds.
result General result for attractors in n-dimensional manifolds.
Let (ρ_λ)_{λ\in Λ} be a holomorphic family of representations of a finitely generated group G into PSL(2,C), parameterized by a complex manifold Λ. We define a notion of bifurcation current in this context, that is, a positive closed current on Λdescribing the bifurcations of this family of representations in a quantit…
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as bifurcation parameter. Our methods are based on well known results from variational bifu…
Ellipsoids host infinitely many minimal tori, bifurcating from a 2-torus orbit.
problem Minimal tori in ellipsoids.
method Analyzing 3D ellipsoids invariant under a 2-torus action.
result Infinitely many distinct minimal tori bifurcate from a 2-torus orbit.
We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a criterion to see that the conformal factors corresponding to the bifurcated metrics must…
We associate to a parametrized family of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index is derived from the index bundle of the linearization of the …
New bifurcation found in perturbations of non-generic closed self-shrinkers.
problem Understanding the behavior of perturbations in non-generic closed self-shrinkers.
method Analyzing the mean curvature flow singularity transitions.
result Different types of singularity transitions based on perturbation direction.
Study describes bifurcations of gradient flows on 2-sphere with holes.
problem Analyzing gradient flows on a 2-sphere with up to six singular points.
method Using separatrix diagrams to specify saddle-node and saddle connections.
result Identified all possible topological structures of bifurcations.
Study shows bifurcation in optimal retirement planning.
problem Optimal consumption and retirement planning model.
method Cobb-Douglas utility, simple model with wealth bifurcation.
result Critical wealth level leads to a continuum of retirement trajectories.
New theory shows how membranes can break symmetry.
problem Understanding symmetry breaking in membranes with boundaries.
method Applied bifurcation theory and reduced membrane equation.
result Existence of symmetry breaking bifurcation in membrane solutions.
New solutions found for Ginzburg-Landau equations on complex manifolds.
problem Finding solutions to Ginzburg-Landau equations on closed manifolds.
method Bifurcation theory applied to Laplace-type operator eigenvalues.
result First nonminimal and irreducible solutions on nontrivial line bundles.
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
problem Detecting P-type bifurcations in signals with unreliable kernel density estimates.
method Create persistence diagrams from single system realization, statistically analyze resulting set, compare point process modeling methods.
result Subsampling outperforms other point process modeling methods in predicting P-type bifurcations.
Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputsnlin.CD
Extremely accurate prediction of dynamical system bifurcations using control inputs.
problem Predicting complex bifurcation structures in dynamical systems.
method Extending extreme learning machines with control inputs to model system dynamics.
result The model can nearly reproduce the entire structure of bifurcations using only a few parameter values.
Study finds multiple periodic solutions to ODEs related to curvature problems.
problem Finding multiple positive periodic solutions to quasilinear ODEs.
method Global bifurcation techniques applied to second order quasilinear ODEs.
result Bifurcation-theoretic proof of nonuniqueness for conformal metrics with constant scalar curvature.
In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay of a control parameter. A single order parameter is introduced by Markovian cha…
We extend the notion of reticular Legendrian unfoldings in order to investigate multi-time bifurcations of wavefronts generated by an r-corner. We give a classification list of generic and stable bifurcations with two time parameter and give all generic figures in the plane and the space.
Study bifurcations of curves on surfaces in Minkowski 3-space.
problem Understanding the behavior of curves on surfaces in Minkowski 3-space.
method Analyzing the degeneracy of induced pseudo metric, discriminant of principal curvatures, parabolic curve, and mean curvature vanishing points.
result Bifurcations of robust features on surfaces in Minkowski 3-space.
Initiated by the work of Uhlenbeck in late 1970s, we study questions about the existence, multiplicity and asymptotic behavior for minimal immersions of closed surface in some hyperbolic three-manifold, with prescribed conformal structure on the surface and second fundamental form of the immersion. We prove several res…
We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on a geodesic ball, whose radius is used as the bifurcation parameter. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.
Paper uses Simulated Bifurcation for quick asset allocation optimization.
problem Optimal asset allocation selection.
method Simulated Bifurcation algorithms applied to 441 S&P500 assets.
result Unrivaled timescale for optimal sub-allocation selection.
Euler-Plateau, with a twistcond-mat.soft
A generalization of the Euler-Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler-Lagrange equations are derived in a parameterized setting and a bifurcation analysis is performed. A pair of dimensionless parameters govern bifurcations from a flat, circular gro…
We give two numerical methods for computing the first bifurcation point for Delaunay nodoids. With regard to methods for constructing constant mean curvature surfaces, we conclude that the bifurcation point in the analytic method of Mazzeo-Pacard is the same as a limiting point encountered in the integrable systems met…
Study on positive solutions of Yamabe-type equation on spheres.
problem Existence and multiplicity of conformal metrics with constant scalar curvature.
method Reduction to an ODE and application of bifurcation theory.
result Existence of degenerate solutions and multiplicity results.
Study describes Morse flows on a torus with up to six singular points.
problem Understanding the structure of Morse flows on a torus with a hole.
method Used separatrix diagrams to describe topological structures and saddle-node bifurcations.
result Identified all possible topological structures of Morse flows with at most six singular points.
The conjugate locus of a point in a surface will have a certain number of cusps. As the point is moved in the surface the conjugate locus may spontaneously gain or lose cusps. In this paper we explain this `bifurcation' in terms of the vanishing of higher derivatives of the exponential map; we der…
We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. Th…
We give a functional analytical proof of the equality between the Maslov index of a semi-Riemannian geodesic and the spectral flow of the path of self-adjoint Fredholm operators obtained from the index form. This fact, together with recent results on the bifurcation for critical points of strongly indefinite functional…
We prove an extension of a celebrated equivariant bifurcation result of J. Smoller and A. Wasserman, in an abstract framework for geometric variational problems. With this purpose, we prove a slice theorem for continuous affine actions of a (finite-dimensional) Lie group on Banach manifolds. As an application, we discu…