**Links and References**

**Books**

Nonlinear Dynamics and Chaos: With Applications 2ed, Strogatz, 2014 (Main text)

Differential Equations, Blanchard, Devaney, Hall (more elementary treatment in the same modern spirit)

Nonlinear Differential Equations and Dynamical Systems, Verhulst (more rigorous treatment in the same modern spirit)

Stability, Instability, and Chaos, Glendinning (more rigorous treatment in the same modern spirit)

Chaos: An Introduction to Dynamical Systems, Alligood, Sauer, Yorke (more focus on discrete dynamical systems)

Online ODE texts

A Primer of Ecology (Gotelli)

**Videos**

Strogatz Cornell lectures based on our main text

Strogatz lab demos

Simulation of bead on a rotating hoop

**Interesting links**

Self-contained proof of the fundamental existence and uniqueness theorem for ODEs (Optional!)

How Populations Grow: The exponential and logistic equations

Dimensional analysis and scaling

More About Nondimensionalization

Buckingham π theorem

Nondimensionalizing a second order ODE

Analytic criterion for bifurcation for x'=f(x)

Single table summary of analytic criterion for bifurcation for x'=f(x)

Baby normal forms (advanced)

Quick review of 2×2 matrices for ODEs

Jordan Canonical Form for 2D matrices

Solving 2x2 systems of linear ODEs

Phase portraits of 2x2 systems of linear ODEs (summary)

Phase portraits of 2x2 systems of linear ODEs (details)

Selected topics in bifurcation theory (advanced, but good discussion of beams)

Imperfect Vaccine Aggravates the Long-standing Dilemma of Voluntary Vaccination

Competition, Coexistence, and Evolution, Ayala (Distinguished GT visitor)

ODE models of chemical reactions

The velocity dependence of aerodynamic drag

How terminal is terminal velocity?

Supercritical bifurcation of a spinning hoop (Physics fans)

A mechanical analog of first and second order phase transitions via bead on a rotating hoop (Physics fans)

The SIR model and the Foundations of Public Health

A damped pendulum forced with a constant torque (experiment and theory)

Very basic model of buckling column (I forget who showed me this)

Synchronized fireflies (Great Smoky Mountains)

The Synchronicity of Firefly Flashing (Stewart)

Control of flashing in fireflies (Buck)

Synchronous Rhythmic Flashing of Fireflies (Buck)

Synchronous Rhythmic Flashing of Fireflies II (Buck)

Toward a Functional Interpretation of Synchronous Flashing by Fireflies (Buck)

An adaptive model for synchrony in the firefly Pteroptyx malaccae (Ermentrout)

Synchronization of pulse-coupled biological oscillators (Strogatz)

Some characteristics and simple types of predation and parasitism (Holling)

Electrical circuits and linear ODEs

Some dynamical models of love (Sprout)

Linear system model of sliding plates

Examples of phase portraits for nonlinear systems in the plane 1 2 3 4 5 6

Conjugate phase portraits of linear systems (McSwiggen and Meyer)

Conjugacy (Rauch)

Linear maps and ODEs

An Undergraduate’s Guide to the Hartman-Grobman and Poincar'e-Bendixon Theorems

Topological Conjugacy and Equivalence and remarks of the Hartman-Grobman theorem

Routh-Hurwitz criterion

Derivation of Lorenz system

Original paper by Lorenz

Video of chaotic waterwheel modeled by Lorenz system

Big O and little o

The Effects of Temperature on the Stability of a Neuronal Oscillator (Winberg)

Introduction to competition (slides from upper level ecology course)

Species Interactions and Competition

Proof of Morse Lemma

Some intuition about gradient systems

Dynamics of Predation

Population Dynamics of Mutualism

Crowd synchrony on the Millennium Bridge

Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis (advanced)

A piecewise linear suspension bridge model: nonlinear dynamics and orbit continuation

Large torsional oscillations in suspension bridges: fixing an old approximation

What to Say About the Tacoma Narrows Bridge to your Introductory Physics Class (an alternative linear model)

Awesome examples of simple closed curves (Ross)

The Jordan Curve Theorem, Formally and Informally (Hales)

Criterion for Hopf bifurcation 1

Criterion for Hopf bifurcation 2

An introduction to the Lorenz system (Lanford)

Physics and Galerkin approximation behind Lorenz model

An introduction to the Lorenz equations (Sparrow)

The Lorenz attractor exists (Tucker)

A rigorous ODE solver and Smale's 14th problem (Tucker)

1 page summary of properties of Lorenz system (Knill)

1 page summary of phase portraits and bifurcations of Lorenz system (Knill)

Preturbulence: A Regime Observed in a Fluid Flow Model of Lorenz (Kaplan and Yorke)

**Software**

pplane and dfield (Java versions) Users manual

Wolfram Alpha

2x2 matrices with Mathematica (1 page)

Brief Mathematica ODE Demo.nb.pdf (2 pages)

The Matlab ODE suite

Elementary Mechanics Using Matlab (good guide to solving problems in mechanics)

Solving ODEs in Matlab

Physical modeling in MATLAB (Downey) free textbook

LSODE

3 lines of Mathematical code to numerically solve x''+sin(x)=0, x(0)=1, x'(0)=-1 and plot solution

7 lines of Matlab code to numerically solve x''+sin(x)=0, x(0)=1, x'(0)=-1 and plot solution

Interactive Differential Equations (applets) These are very insightful but require you modify the JAVA security settings

Differential equations With Matlab (good book with intro to numerical issues solving ODEs)

Mathematica Notebook to study motion of particle in double well potential and undamped pendulum pdf version

Two disasters caused by computer arithmetic mistakes