Bifurcations Part 3 Pitchfork Bifurcation

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=W8rnh14bChA

A pitchfork bifurcation occurs where a single fixed point splits into three of alternating stability type. We motivate this with the snap-through buckling of a beam. From 'Nonlinear Dynamics and Chaos'. Next, robustness of bifurcations • Bifurcations Part 4- Robustness of Bi... • ► Bifurcation videos • Saddle-node bifurcation • Bifurcations Part 1, Saddle-Node Bifu... • Trans-critical bifurcation • Bifurcations Part 2- Transcritical Bi... • Pitchfork bifurcation • Bifurcations Part 3- Pitchfork Bifurc... • Robustness of bifurcations • Bifurcations Part 4- Robustness of Bi... • ► Online course playlist • https://is.gd/NonlinearDynamics • ► Subscribe https://is.gd/RossLabSubscribe • ► Dr. Shane Ross, Virginia Tech professor (Caltech PhD) • http://chaotician.com • ► In-depth mathematical discussion of bifurcations • Bifurcation Theory: Saddle-Node, Hopf... • ► Course lecture notes (PDF) • https://is.gd/NonlinearDynamicsNotes • Reference: Steven Strogatz, Nonlinear Dynamics and Chaos , Chapter 3: Bifurcations • Videos of snap-through from • 'Dynamics of snapping beams and jumping poppers' by A. Pandey, D. E. Moulton,, D. Vella, and D. P. Holmes [2014] EPL (EuroPhysics Letters) 105, 24001. • http://doi.org/10.1209/0295-5075/105/... • • supercritical bifurcation subcritical bifurcations buckling beam model change of stability nonlinear dynamics dynamical systems differential equations dimensions phase space Poincare Strogatz graphical method Fixed Point Equilibrium Equilibria Stability Stable Point Unstable Point Linear Stability Analysis Vector Field One-Dimensional 1-dimensional Functions • #NonlinearDynamics #Bifurcations #pitchfork #buckling #snapthrough #pitchforkbifurcation #robust #StructuralStability #DifferentialEquations #dynamics #dimensions #PhaseSpace #Poincare #Strogatz #graphicalmethod #FixedPoints #EquilibriumPoints #Stability #StablePoint #UnstablePoint #Stability #LinearStability #LinearStabilityAnalysis #StabilityAnalysis #VectorField #OneDimensional #Functions

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