Explaining Bifurcations
نویسنده
چکیده
This paper will introduce the topic of dynamical systems with both discrete and continuous time variables. Fixed points will be discussed, along with their properties such as stability or topological type. The paper will continue on to define the concept of hyperbolicity and its relevance in determining the structural stability of the system. It will conclude with a definition of a bifurcation as well as a brief description of bifurcation theory and its applications.
منابع مشابه
Border collision bifurcations in two-dimensional piecewise smooth maps
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and clas...
متن کاملIntroduction to bifurcation theory
The theory of bifuxcation from equilibria based on center-manifold reduction and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail:...
متن کاملBifurcations in One-Dimensional Piecewise Smooth Maps—Theory and Applications in Switching Circuits
The dynamics of a number of switching circuits can be represented by one-dimensional (1-D) piecewise smooth maps under discrete modeling. In this paper we develop the bifurcation theory of such maps and demonstrate the application of the theory in explaining the observed bifurcations in two power electronic circuits.
متن کاملFlow in experimental berry aneurysms: method and model.
This study addresses two basic questions: What are the flow dynamics in aneurysms? Can these flows be modified to enhance retention of adhesive? Using Pyrex glass bifurcations, fluid flow was studied in a variety of aneurysms placed at varying positions around the bifurcations. Indicators injected into the slipstreams were recorded and studied both by stop-frame high-speed movie analysis and wi...
متن کاملCosmic Symmetry-breaking, Bifurcation, Fractality and Biogenesis
This paper explores the non-linear quantum foundations of biogenesis in interactive bifurcations between the properties of the elements, sourced in the transitions induced by cosmic symmetry-breaking [King 1978]. The key interactions forming the biogenic pathway are modeled in terms of interactive quantum bifurcations explaining why the bioelements play the interactive role they do and why cent...
متن کاملSimulation study of Hemodynamic in Bifurcations for Cerebral Arteriovenous Malformation using Electrical Analogy
Background and Objective: Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are...
متن کامل