Nonlinear Dynamics amp Chaos Introduction Lecture 1 of a Course

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=bOpxQ7hGpmM

Nonlinear Dynamics and Chaos (online course). Introduction and historical overview of nonlinear dynamics and chaos for those new to the subject. See the rest of the course videos https://is.gd/NonlinearDynamics • ► Next, the big picture of dynamics • • Big Picture of Dynamics Its Applica... • ► From Nonlinear Dynamics and Chaos (online course) • Course playlist • Nonlinear Dynamics and Chaos | Online... • ► Prerequisites for course: • You should have some familiarity with linear algebra and calculus. But you do not need expertise in mathematics, physics, engineering, or biology. • ► Dr. Shane Ross, Chaotician, Virginia Tech professor (Caltech PhD) • Subscribe https://is.gd/RossLabSubscribe • ► Introduction to the instructor, Dr. Shane Ross • • Professor Shane Ross Introduction • ► Follow me • / rossdynamicslab • ► Other key topics in this course • 1D ODE dynamical systems • Graphical Analysis of 1D Nonlinear ODEs • Bifurcations • Bifurcations Part 1, Saddle-Node Bifu... • Bead in a rotating hoop • Bead in a Rotating Hoop, Part 1- Deri... • 2D nonlinear systems • 2D Nonlinear Systems Introduction- Be... • Limit cycles • Limit Cycles, Part 1: Introduction ... • 3D Lorenz equations • 3D Systems, Lorenz Equations Derived,... • Discrete time maps • Maps, Discrete Time Dynamical Systems... • Self-similarity in bifurcation diagrams • Logistic Map, Part 2: Bifurcation Dia... • Fractals • Fractals: Koch Curve, Cantor Set, Non... • Geometry of strange attractors • Geometry of Strange Attractors: Chaos... • Horseshoe map, symbolic dynamics • Horseshoe Map - Essence of Chaos, Sym... • ► Course lecture notes (PDF) • https://is.gd/NonlinearDynamicsNotes • ► Research website for ‪@ProfessorRoss‬ • http://chaotician.com • Reference: Steven Strogatz, Nonlinear Dynamics and Chaos , Chapter 1: Overview • ► Related Courses Series Playlists by Dr. Ross • 📚Nonlinear Dynamics Chaos • https://is.gd/NonlinearDynamics • 📚Lagrangian 3D Rigid Body Dynamics • https://is.gd/AnalyticalDynamics • 📚Hamiltonian Dynamics • https://is.gd/AdvancedDynamics • 📚Center Manifolds, Normal Forms, Bifurcations • https://is.gd/CenterManifolds • 📚3-Body Problem Orbital Dynamics • https://is.gd/3BodyProblem • 📚Space Manifolds • https://is.gd/SpaceManifolds • 📚Space Vehicle Dynamics • https://is.gd/SpaceVehicleDynamics • Smale Horseshoe map Horseshoe-type forced damped double-well Duffing oscillator ball cart Moon's beam Rossler attractor equation Poincare Lyapunov exponent unstable supercritical topological structural stability systems differential Strogatz graphical method Fixed Point Equilibria Functions Hamilton topology Synchrony strange Homoclinic trellis Time-dependent fractal basin of attraction boundary forced damped double-well ball in cart Moon's beam Rossler Mandelbrot set capacity self-similar dimension box-counting dimension correlation dimension period doubling analog logistic largest Liapunov exponent fractal dimension of Edward Lorenz box-counting dimension crumpled paper focus supercritical subcritical structural epsilon of multiple scales driven Liapunov autonomous plane robustness fragility cusp unfolding perturbations structural critical supercritical differential phase Linear Analysis Vector Field Two-Dimensional 2-dimensional Verhulst Oscillators Synchrony dynamics equations convection Michel Henon • #NonlinearDynamics #DynamicalSystems #AppliedMath #ChaosTheory #Bifurcation #DifferentialEquations #Dynamics #mathematics #chaos #chaotician #IanMalcolm #JurrasicPark #ChaoticDynamics #butterfly #ButterflyEffect #ButterflyDiagram #Newton #Poincare #Lorenz #LorenzEquations #LorenzAttractor #Attractor #Duffing #StrogatzBulldog #math #FreeCourses #OnlineCourse #VirginiaTech #Caltech #Hurricanes #LagrangianCoherentStructures #HenonMap #HenonAttractor #Fractals #Rossler #Mandelbrot #MandelbrotSet #Universality #PeriodDoubling #Bifurcations #LogisticMap #DifferenceEquation #PoincareMap #Lyapunov #HopfBifurcation #NonlinearOscillators #LimitCycle #Oscillations #VectorFields #topology #geometry #IndexTheory #EnergyConservation #Hamiltonian #Streamfunction #Gradient #PopulationBiology #FixedPoint #DifferentialEquations #SaddleNode #Eigenvalues #HyperbolicPoint #NonHyperbolicPoint #CuspBifurcation #CriticalPoint #buckling #PitchforkBifurcation #robust #StructuralStability #dimensions #PhaseSpace #PhasePortrait #PhasePlane #Strogatz #Wiggins #VectorField #GraphicalMethod #FixedPoints #EquilibriumPoints #NonlinearODEs #StablePoint #UnstablePoint #Stability #LinearStability #StabilityAnalysis #VectorField #PopulationDynamics #Logistic #Pendulum #Poincare #mathematicians #maths #mathstudents #mathematician #mathfacts #mathskills #mathtricks #KAMtori

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