Chaos and System dynamics Leon Chang

Edward Lorenz In the early 1960's using a simple system of equations to model convection in the atmosphere, Edward Lorenz, an MIT meteorologist, ran headlong into "sensitivity to initial conditions". In the process he sketched the outlines of one of the first recognized chaotic attractors.

The Butterfly Effect The "Butterfly Effect" is the propensity of a system to be sensitive to initial conditions.Such systems over time become unpredictable,this idea gave rise to the notion of a butterfly flapping it's wings in one area of the world,causing a tornado or some such weather event to occur in another remote area of the world

Lorenz model

Lorenz waterwheel

Lorenz model by system dynamics

Lorenz result r=28.00

1: r= : r= : r=28.03 Lorenz result comparison

Strange attractor by X-Y

Strange attractor by Y-Z

Strange attractor by X-dX/dt

Lorenz attractor

成長上限

成本與投資不足

Using system dynamics to analyse interactions in duopoly competition Petia Sicea, Erik Mosekildeb, Alfredo Moscardinic, Kevin Lawlerc and Ian Frenchd* System Dynamics Review Vol. 16, No. 2, (Summer 2000): 113–133

Phase plane portrait (FQ against CQ) illustrating the singleperiod limit cycle behaviour observed for a = 2 and c = 0.1

Phase plane portrait (FQ against CQ) illustrating the chaotic behaviour for a = 2 and c = 0.4

Plot of D over the period 750 to 7000 months; the straight line, which has slope 0.005, represents the ‘best fit’ over the period 1500 to 4500

Fractal