the butterfly effect

Weather is a chaotic phenomenon. This means that minor changes in some conditions may lead to huge differences in weather patterns.

With the installation of a large number of meteorological observation stations, we collect data on what is happening in the atmosphere and so we can make short-term weather forecasts.

We can not predict weather in the long run because we can not know precisely on the scale of the millimeter, what happens every time and everywhere in the atmosphere.

The phenomenon of the butterfly is a poetic transfer to the theory of chaos. Describes this delicate dependence on the original conditions. If a butterfly moves its wings to some area, this may be the reason for creating a hurricane thousands of miles away. Of course this fact will never prove it, but it is possible and it can happen.

ACTIVITY 1

We consider a variable X, whose current value is known. If we also know how it evolves over time, we can say what its value will be a little later (after Δt). If we call the current time t1, then we can say that:

t2 = t1 + Δt,

t3 = t2 + Δt, ... etc

In other words, we can use the value of variable X at any time t, X(t), to calculate its value after time Δt, X(t + 1)

The following equation (accounting equation) describes the particular way in which the variable x develops (each subsequent value of x depends on its previous value):

X(t + 1) = k X(t ) [1 - X(t)]

Since time-varying variables evolve in a similar fashion (their later values ​​depend on the previous ones), this equation is very useful for describing the time course of the weather.

But the variable X is distinct because we do not study its values ​​continuously at any time but at regular intervals. The above accounting equation describes the evolution of a dynamic discrete time system and is, as we say, a nonlinear difference equation.

In the spreadsheet with which you will work, we have set the parameter k, and the initial value of variable X at t= 0. By altering their values, you will investigate the result for X values ​​after 60 reps. Follow the instructions in the worksheet and reference. To open the interactive spreadsheet clik here . In order to work properly you must download the spreadsheet and then open it whith MS Excel

ACTIVITY 2

The atmosphere is a complex system. Complex is the system of interacting elements whose collective behavior can not be described by the simple sum of the behavior of its components. For example, the colony of the ants is a complex system.

However, we should not confuse complex systems with complicated systems. An example of a complicated system is a car engine or a computer processor.

What is the difference between a complicated system and a complex system?

Look for other systems that would characterize them complex or complicated. Discuss the function (operation) and behavior of these systems with your peers and your class teacher and record the results.