Dynamical Systems

Dynamical Systems

In System Dynamics simulation allows for paths to the variables included in any model by applying numerical integration techniques. However, these paths are never interpreted as predictions, but as projections or trends. The purpose of the System Dynamics models is, as in all soft systems methodologies, to understand how the structure of the system is responsible for his behavior. This understanding should normally produce a favorable environment to determine actions that can improve system performance or solve the identified problems. The advantage of system dynamics is that these actions can be simulated at low cost, making it possible to assess their performance without putting them into practice on the real system.

In System dynamics the simulation allows to obtain paths for the variables included in any model by means of the application of technologies of numerical integration. Nevertheless, these paths are never interpreted as predictions, but as projections or trends. The object of the models of System dynamics is, since it happens in all the methodologies of soft systems, to manage to understand how the structure of the system is responsible for his behavior. This comprehension normally must generate a favorable frame for the determination of the actions that could improve the functioning of the system or solve the observed problems.

The advantage of the System dynamics consists in that these actions can be simulated to low cost, with what it is possible to value his results without need to put them into practice on the royal system.

A dynamic system is a complex system, which presents a change or evolution of his condition in a time, the behavior in the above mentioned condition can be characterized determining the limits of the system, the elements and his relations; of this form it is possible to elaborate models who seek to represent the structure of the same system.

On having defined the limits of the system there is done, first, a selection of those components that help to generate the manners of behavior, and then the space decides where the study will be carried out, omitting all kinds of irrelevant aspects.
 As for the production of the models, the elements and his relations, it is necessary to to bear in mind:

A system is formed by a set of elements in interaction.
 The behavior of the system can appear across causal graphs.
 There are several types of variables: exogenous variables (they are those that concern the system without this one provokes them) and the endogenous variables (they concern the system but this one yes it provokes

An example of a dynamic system can be seen in a species of fish that is reproduced in such a way that this year the quantity of fish is Xk, next year will be Xk + 1. Hereby we can put names to the quantities of fish that will exist every year, this way: initial year X0, the first year X1........... ......, year k Xk.

 Since it is possible to observe:, it is fulfilled for any year k; which means that the quantity of fish can decide if there is known the quantity of the previous year. Consequently this equation represents a dynamic system.