Bifurcations in 2D, Part 3: Hopf Bifurcation Physical Examples

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 https://youtu.be/iphb2GlNtCk ► Playlist 'Nonlinear Dynamics and Chaos' (online course) https://www.youtube.com/playlist?list=PLUeHTafWecAUqSh3Gy0NNr7H3OsXoC-aK ► Bifurcations in 2D Zero eigenvalue bifurcations https://youtu.be/pl3byZQkVd8 Hopf bifurcation theory https://youtu.be/20O6v1X92P4 Hopf physical examples https://youtu.be/4vOC7zw2YME Bifurcations of limit cycles https://youtu.be/iphb2GlNtCk ► Bifurcations in 1D (the zero eigenvalue bifurcations) Saddle-node https://youtu.be/BBd68_q3Dgg Trans-critical https://youtu.be/65ZKdscURXg Pitchfork https://youtu.be/W8rnh14bChA Robustness https://youtu.be/oQnWVmt_A3U ► Additional background on 2D dynamical systems Phase plane introduction https://youtu.be/U4IM7HFzcuY Classifying 2D fixed points https://youtu.be/7Ewe_tVa5Fs Gradient systems https://youtu.be/uGUzPZzvPWQ Index theory https://youtu.be/bO8FxxpocNQ Limit cycles https://youtu.be/9rVscJwDpBo Averaging theory https://youtu.be/UzQU1nyM-No ► Advanced lecture on Hopf bifurcations https://youtu.be/MgmutdItm8Q ► Dr. Shane Ross, Virginia Tech professor (Caltech PhD) Subscribe https://is.gd/RossLabSubscribe​ ► Follow me on Twitter https://twitter.com/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/Belousov–Zhabotinsky_reaction References: Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 8: Bifurcations Revisited Kirubakaran Purushothaman, Aeroelastic flutter demonstration using venetian blind strips, https://youtu.be/r681ySdC1Zw ICIQchem, Oscillating reactions – The chemical clock, https://youtu.be/PYxInARIhLY Jonathan Mitchell, When Math Drops the Bass - Hopf Bifurcation, https://youtu.be/EtjdjrKu9Jk​ 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