Bifurcations in 2D Part 3 Hopf Bifurcation Physical Examples

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Physical examples of Hopf bifurcation, where a limit cycle is created from a fixed point: flutter of window blinds and airplane wings, oscillating chemical reactions (Belousov-Zhabotinsky reaction), gliding of flying squirrels. The Hopf bifurcation can occur in high dimensional systems and is robust to perturbations. Hopf bubbles. Global versus local stability of limit cycles. • ► Next, global bifurcations in 2D • • Bifurcations in 2D, Part 4: Global Bi... • ► Playlist 'Nonlinear Dynamics and Chaos' (online course) • • Nonlinear Dynamics and Chaos | Online... • ► Bifurcations in 2D • Zero eigenvalue bifurcations • Bifurcations in 2D, Part 1: Introduct... • Hopf bifurcation theory • Bifurcations in 2D, Part 2: Hopf Bifu... • Hopf physical examples • Bifurcations in 2D, Part 3: Hopf Bifu... • Bifurcations of limit cycles • Bifurcations in 2D, Part 4: Global Bi... • ► Bifurcations in 1D (the zero eigenvalue bifurcations) • Saddle-node • Bifurcations Part 1, Saddle-Node Bifu... • Trans-critical • Bifurcations Part 2- Transcritical Bi... • Pitchfork • Bifurcations Part 3- Pitchfork Bifurc... • Robustness • Bifurcations Part 4- Robustness of Bi... • ► Additional background on 2D dynamical systems • Phase plane introduction • Phase Portrait Introduction- Pendulum... • Classifying 2D fixed points • Classifying Fixed Points of 2D Systems • Gradient systems • Gradient Systems - Nonlinear Differen... • Index theory • Index Theory for Dynamical Systems, P... • Limit cycles • Limit Cycles, Part 1: Introduction ... • Averaging theory • Averaging Theory for Weakly Nonlinear... • ► Advanced lecture on Hopf bifurcations • • Hopf Bifurcation Example- Normal Form... • ► Dr. Shane Ross, Virginia Tech professor (Caltech PhD) • Subscribe https://is.gd/RossLabSubscribe • ► Follow me on Twitter • / rossdynamicslab • ► Make your own phase portrait • https://is.gd/phaseplane • ► Course lecture notes (PDF) • https://is.gd/NonlinearDynamicsNotes • ► Courses and Playlists by Dr. Ross • 📚Attitude Dynamics and Control • https://is.gd/SpaceVehicleDynamics • 📚Nonlinear Dynamics and Chaos • https://is.gd/NonlinearDynamics • 📚Hamiltonian Dynamics • https://is.gd/AdvancedDynamics • 📚Three-Body Problem Orbital Mechanics • https://is.gd/SpaceManifolds • 📚Lagrangian and 3D Rigid Body Dynamics • https://is.gd/AnalyticalDynamics • 📚Center Manifolds, Normal Forms, and Bifurcations • https://is.gd/CenterManifolds • • BZ reaction: A chemical oscillator — this chemical reaction changes color periodically, doesn’t settle down to equilibrium. It’s the Belousov–Zhabotinsky reaction, or BZ reaction, and mathematically it’s a limit cycle that arises from a Hopf bifurcation. • BZ reaction: https://en.wikipedia.org/wiki/Belouso... • References: • Steven Strogatz, Nonlinear Dynamics and Chaos , Chapter 8: Bifurcations Revisited • Kirubakaran Purushothaman, Aeroelastic flutter demonstration using venetian blind strips, • • Aeroelastic flutter demonstration usi... • ICIQchem, Oscillating reactions – The chemical clock, • Oscillating reactions – The chemical ... • Jonathan Mitchell, When Math Drops the Bass - Hopf Bifurcation, • When Math Drops the Bass - Hopf Bifur... • • stable focus unstable focus supercritical subcritical topological equivalence genetic switch structural stability Andronov-Hopf Andronov-Poincare-Hopf small epsilon method of multiple scales two-timing Van der Pol Oscillator Duffing oscillator nonlinear oscillators nonlinear oscillation nerve cells driven current nonlinear circuit glycolysis biological chemical oscillation adenosine diphosphate ADP fructose Liapunov gradient cylinder bifurcation robustness fragility cusp unfolding perturbations structural emergence critical point critical slowing down supercritical bifurcation subcritical bifurcations buckling beam model change of stability nonlinear dynamics dynamical systems differential equations dimensions phase space Poincare Strogatz graphical method Fixed Equilibrium Equilibria Stability Stable Unstable Linear Analysis Vector Field Two-Dimensional 2-dimensional Functions Hamiltonian Hamilton streamlines weather vortex dynamics point vortices pendulum Newton's Second Law Conservation of Energy topology Verhulst • #NonlinearDynamics #DynamicalSystems #Bifurcation #Hopf #HopfBifurcation #NonlinearOscillators #AveragingTheory #LimitCycle #Oscillations #nullclines #RelaxationOscillations #VanDerPol #VanDerPolOscillator #LimitCycles #VectorFields #topology #IndexTheory #EnergyConservation #Hamiltonian #Streamfunction #Streamlines #Vortex #SkewGradient #Gradient #PopulationBiology #FixedPoint #DifferentialEquations #SaddleNode #Eigenvalues #HyperbolicPoints #NonHyperbolicPoint #CuspBifurcation #CriticalPoint #buckling #PitchforkBifurcation #robust #StructuralStability #DifferentialEquations #dynamics #dimensions #PhaseSpace #PhasePortrait #PhasePlane #Poincare #Strogatz #Wiggins #VectorField #GraphicalMethod #FixedPoints #EquilibriumPoints #Stability #NonlinearODEs #StablePoint #UnstablePoint #Stability #LinearStability #LinearStabilityAnalysis #StabilityAnalysis #VectorField #TwoDimensional #Functions #PopulationGrowth #DynamicalSystems #PopulationDynamics #Population #Logistic #GradientSystem #GradientVectorField #Cylinder #Pendulum #Newton #LawOfMotion

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