相关论文: The Pitchfork Bifurcation
Generic results for degenerate Chenciner (generalized Neimark-Sacker) bifurcation are obtained in the present work. The bifurcation arises in two-dimensional discrete-time systems with two independent parameters. We define in this work a…
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.
We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature (curve-shortening) flow. We obtain the bifurcations of the period two orbits and some special…
We extend Natural Deduction for intuitionistic logic with a third introduction rule for the disjunction, $\vee$-i3, with a conclusion $\Gamma\vdash A\vee B$, but both premises $\Gamma\vdash A$ and $\Gamma\vdash B$. This rule is admissible…
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…
In this brief note we critically examine the process of partial and of total differentiation, showing some of the problems that arise when we relate both concepts. A way to solve all the problems is proposed.
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal…
We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
We study some global aspects of the bifurcation of an equivariant family of volume-contracting vector fields on the three-dimensional sphere. When part of the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the…
We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
We explore taxicab conic sections from the perspective of slicing taxicab cones by planes, as opposed to the more well-studied approach from the perspective of distance formulations. After establishing a significant amount of structural…
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
The understanding and prediction of sudden changes in flow patterns is of paramount importance in the analysis of geophysical flows as these rare events relate to critical phenomena such as atmospheric blocking, the weakening of the Gulf…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…