Essays about: "Bifurcation theory"

Showing result 1 - 5 of 8 essays containing the words Bifurcation theory.

1. 1. Gravity water waves over constant vorticity flows: from laminar flows to touching waves

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Author : Francisco Gonçalves Jorge Dias de Carvalho; [2023]
   Keywords : Partial differential equations; Water waves; Euler equations; Free boundary problem; Bifurcation theory; Nonlinear functional analysis; Hilbert transform; Mathematics and Statistics;

   Abstract : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. READ MORE

3. 2. Numerical Solutions and Parameter Sensitivity of the Lorenz System

   University essay from KTH/Skolan för teknikvetenskap (SCI)

   Author : Eira Larsson; Vilmer Ström; [2023]
   Keywords : Lorenz system; Dynamic Bifurcation; Periodic Parameter Perturbation; Chaos; Runge-Kutta; Shadowing Lemma;

   Abstract : In chaos theory there are many different problems still unsolved. One of which is the optimization of infinite time average functionals on manifolds. To try one of the different tools to solve this problem we want to find stable manifolds in chaotic dynamical systems. READ MORE

4. 3. Feigenbaum Scaling

   University essay from Linnéuniversitetet/Institutionen för matematik (MA)

   Author : Janek Sendrowski; [2020]
   Keywords : Feigenbaum; Feigenbaum constant; Feigenbaum point; superstable; self-similarity; fractals; final-state diagram; logistic map; period-doubling operator; linearized period-doubling operator; Cantor set; Sharkovsky sequence; Chebyshev interpolation; stable manifold; unstable manifold; orbits; fixed points; scaling factor; pitchfork bifurcation; cobweb plot; renormalization; iterates; one-hump map; unimodal map; bifurcation cascade; Feigenbaum universality; chaos theory; spectrum; generalized Feigenvalues; bifurcation points; superstable points; fixed function; universal function; eigenvalues; eigenvectors; eigenfunctions; universality conditions; Schwarzian derivative; Newton’s method; power method; Arnoldi’s method; attractive fixed point; repellent fixed point; Banach fixed-point theorem; collocation method; functional analysis; topology;

   Abstract : In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. READ MORE

5. 4. Analysis of an Attractor Neural Network Model for Working Memory: A Control Theory Approach

   University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

   Author : Gianluca Villani; [2019]
   Keywords : ;

   Abstract : Working Memory (WM) is a general-purpose cognitive system responsible for temporaryholding information in service of higher order cognition systems, e.g. decision making. READ MORE

6. 5. Koopman mode analysis of the side-by-side cylinder wake

   University essay from KTH/Mekanik

   Author : Jimmy Röjsel; [2017]
   Keywords : Bluff body; wake flow; Side-by-side cylinder wake; Flip-op instability; Modal analysis; Koopman operator; Koopman mode decomposition;

   Abstract : In many situations, fluid flows can exhibit a wide range of temporal and spatial phenomena. It has become common to extract physically important features, called modes, as a first step in the analysis of flows with high complexity. READ MORE