Bifurcations Part 1 SaddleNode Bifurcation

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=BBd68_q3Dgg

Bifurcations are a qualitative change in the dynamics of a system as a parameter is varied, for instance, fixed points disappear and new ones emerge. We focus on the saddle-node bifurcation, the main mechanism for the creation and destruction of new equilibrium points. From 'Nonlinear Dynamics and Chaos' (online course). Next, transcritical bifurcation • Bifurcations Part 2- Transcritical Bi... • ► CORRECTION at 6:50 Wrong sign under square-root. For x' = r + x^2, the fixed points are at x = +/- sqrt(-r) • ► Other bifurcation topics • transcritical bifurcation • Bifurcations Part 2- Transcritical Bi... • pitchfork bifurcation • Bifurcations Part 3- Pitchfork Bifurc... • robustness of bifurcations • Bifurcations Part 4- Robustness of Bi... • bifurcations in 2D systems • Bifurcations in 2D, Part 1: Introduct... • ► 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... • ► From 'Nonlinear Dynamics and Chaos' • Online course playlist https://is.gd/NonlinearDynamics • ► Subscribe to Ross Dynamics Lab • https://is.gd/RossLabSubscribe • ► Dr. Shane Ross, Virginia Tech professor (Caltech PhD) • http://chaotician.com • ► Course lecture notes (PDF) • https://is.gd/NonlinearDynamicsNotes • ► A more in-depth mathematical discussion of bifurcations • • Bifurcation Theory: Saddle-Node, Hopf... • Reference: Steven Strogatz, Nonlinear Dynamics and Chaos , Chapter 3: Bifurcations • ► 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 • • bifurcation bifurcations saddle-node blue sky 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 #DynamicalSystems #Bifurcations #saddlenode #blueskybifurcation #turningpoint #saddlenodebifurcation #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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