General 2D DS

Strogatz Part Two: Two-dimensional Flows

SHO

Example 5.1.2(a) Stable node@origin

Example 5.1.2(b) Stable star@origin

Example 5.1.2(c) Stable node@origin

Example 5.1.2(d) Stable node@origin

Example 5.1.2(e) Stable node@origin

Example 5.2.1 saddle@origin

Example 5.2.4 unstable spiral@origin

Example 5.2.4nstable spiral@origin

Exercisae 5.3.4 Fire and Water love affairs: do opposites attract?

Strogatz (Ch 6,7,8) Nonlinear System Trajectories

Fields of the form x'=f(x,y),y'=g(x,y) can be treated as linear systems via the trick of noting that a=f(x,y)/x,b=f(x,y)/y,c=g(x,y)/x,d=g(x,y)/y.However,the origin is not necessarily a fixed point.

Example 6.1.1 Saddle

Example 6.3.1 Stable node and saddles

Example 6.3.2 Spiral

Example 6.5.2 Stable center: double well potential V[x]=-Integral[f[x]]=-Int[x-x^3] (ammonia inversion)

Example 6.6.1 Stable centers and saddles

Example 6.7 Stable centers and saddles (damped pendulum)

Duffing Equation

Zimmerman & Olness Problem 4.3.4: damped HO with driving force (pushed child on a swing)

Example 7.1.2 van der Pol oscillator

Example 7.3.3 Glycolysis oscillations

Nullclines and bifurcations:HSD Exm p.190

Example 8.1.1 Gene expression

Example 8.3.2 Chemical oscillations