Chaos and System dynamics.pptVIP

Chaos and System dynamics Leon Chang Edward Lorenz The Butterfly Effect Lorenz model Lorenz waterwheel Lorenz model by system dynamics Lorenz result Lorenz result comparison Strange attractor by X-Y Strange attractor by Y-Z Strange attractor by X-dX/dt 成長上限 成本與投資不足 Using system dynamics to analyse interactions in duopoly competitionPetia Sicea, Erik Mosekildeb, Alfredo Moscardinic, Kevin Lawlerc and Ian Frenchd*System Dynamics Review Vol. 16, No. 2, (Summer 2000): 113–133 Fractal * * In the early 1960s 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 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 its wings in one area of the world,causing a tornado or some such weather event to occur in another remote area of the world r=28.00 1: r=28.00 2: r=28.01 3: r=28.03 Lorenz attractor Phase plane portrait (FQ against CQ) illustrating the singleperiod limit cycle behaviour observed for a = 2 and c = 0.1