Dynamical systems and system dynamics models

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Re: Dynamical systems and system dynamics models

Postby Sangdon Lee » Tue May 25, 2010 4:01 pm

>>I am wondering about the relationship between "dynamical systems" and "system dynamics models". The >>latter describe "feedback-driven" systems. If the "dynamical" essence of a system is generated inside the >>system (otherwise, would it be a system at all?), then I'm tempted to think that any "dynamical system" >>can be described as a "feedback-driven" system and thus represented by a "system dynamics model".

I’m an engineer who has some experience on both “dynamical system” and “System Dynamics.” Mathematically speaking, “dynamical system” and “System Dynamics” are identical, “ordinary differential equations (ODE)”. In engineering disciplines, “system dynamics” and “dynamic systems” are used interchangeably. Stock and flow are called “state” and “derivative” in ODE, respectively.

Even though they are mathematically identical, I see “gigantic” difference between them. Thinking in terms of stock and flow make it possible to build a dynamical model within the realm of everybody without going through "advanced" mathematics in a "graduate" school.

Many books for dynamical system (e.g., feedback control system, etc), focus on “how to solve the ODE”. But those books hardly talk about how to formulate a mathematical model (thus understanding an issue in a time-varying way and thinking in terms of stock & flow and feedback loops) before solving a "given" model with a computer.

>>Experimental evidence suggests that usually there is little awareness of loops and (for instance) exposure to simulators does not augment this awareness.

I found that many engineers who studied and work on dynamical system hardly think a system as a feedback structure nor stock and flow thinking. They know how to solve the ODE (once the mathematical problem is "given") using Matlab.

This seemingly small difference in notation (stock & flow diagram rather than derivatives) is so “gigantic” that even elementary students can build and understand the n-th order ODE!

Can we see the stock & flow and feedback loops from the following ODE model (i.e., predator and prey model)? More importantly, can we formulate such a model?

dx\dt=a*x-b*x*y
dy\dt=c*x*y-d*y

One comment is that SD is ODE, however, a few phenomena such as fluid dynamics, thermo dynamics, etc, in engineering cannot be expressed with ODE. They require “partial” differential equation, which is very difficult to express in ODE (thus SD) due to infinitely many states (stocks).

Sangdon Lee,
GM Tech. Center, USA.
Sangdon Lee
 
Posts: 9
Joined: Wed Jul 22, 2009 7:28 am

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