Nonlinear Dynamics & Chaos Introduction- Lecture 1 of a Course

► Next, the big picture of dynamics

► From Nonlinear Dynamics and Chaos (online course)

► 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)

► Introduction to the instructor, Dr. Shane Ross

► Follow me

► Other key topics in this course

► Course lecture notes (PDF)

► Research website for @ProfessorRoss

Reference: Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 1: Overview

► *Related Courses & Series Playlists by Dr. Ross*

📚Nonlinear Dynamics & Chaos

📚Lagrangian & 3D Rigid Body Dynamics

📚Hamiltonian Dynamics

📚Center Manifolds, Normal Forms, & Bifurcations

📚3-Body Problem Orbital Dynamics

📚Space Manifolds

📚Space Vehicle Dynamics

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

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[AnuragSharma-aka-sheiroo]

After every lecture I finish I will post a comment, as a form of staying motivated to finish this series. Great historical introduction. Good beginning!

[PaulElmont-fdxc]

Fascinating! I thank you so much for sharing these videos with us.

[jjpark]

This is a fantastic series, thank you so much. You have a way of explaining everything in an intuitive (and humorous) way. I was able to kickstart my phd studies thanks to these videos, having no background in complex systems.

[marcopivetta]

this topic is FASCINATING to me. i really wish i had a deeper knowledge of the math, but the core principles are surprisingly simple to grasp with the bare minimum understanding of calculus (so far)

[BruinChang]

Hello, Prof. Ross,

You mentioned hurricane in the video, and I am curious the real cause of the swirl of a hurricane😮. The coriolis force is said to make hurricane have a vortex or swirl. However, Coriolis force is a pseudo force in a rotational frame. When looking a hurricane from the outer space, a hurricane still has a swirl. Is there any real forces behind the phenomenon ?

Thanks a lot.

[cisp]

Thank you very much, professor Ross, for uploading these valuable lectures on youtube. I am studying Strogatz's book, and these lectures help a lot and make it much much more enjoyable.

[marymostafa]

Great work; do you have any videos about symmetry- breaking bifurcation or synchrony breaking bifurcation?

[marcopivetta]

20:17 - 20:27
LMAO blink twice if a computer is threatning you!

[cavalier]

Lol...I read Jurassic Park when I was 12...saw the movie when it came out. Was scared, so I didn't pay it much attention till later....revisited the books, and realized I had subconsciously applied these principles so figured I better learn what I'm talking about

[ThontiBeeraiahaed]

Is stochastic and random different, if yes how ? could you please explain with examples for each other

[wHaTsThIsThInGdO]

What if you can count on this being -1 like in euler equation

[williamschacht]

Newton discovered, not invented, ODEs, LOL. And he didn't give up on the 3-body problem. He just didn't have the proper mathematical tools. 🙂 🙂

Edit: 2-D? Should those "Poincare trajectories" cross like that? Hopefully I'll find out later.

[DrMerle-gwwj]

Well, the first lecture in the series is a lot of drivel. I'll see if there is anything of worth in the second lecture.