7.3 LIMIT CYCLE
 
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·
 System description
·
 Introduction
·
 Model
·
 View
   
 
   
Fig. 7.2: View of the virtual-lab.
    
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System description
 
This virtual-lab illustrates the concept of "limit cycle", by using the following mathematical model:
 

The initial conditions are the following:
 
For any initial values of and (except ), it is satisfied that if , then .
The limit cycle is a circle centered at the origin with radius 1 (i.e., the unit circle).
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Introduction
 
The Introduction panel of the virtual-lab is shown in Fig. 7.18.
 
Fig. 7.18: Introduction of the virtual-lab.
 
The mathematical expressions are images. In order to insert a image in a Introduction page, click on Insert on the menu bar and next click on Image (see Fig. 7.19).
 
Fig. 7.19: Inserting a image.
 
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Model
 
The mathematical model is composed of the two following equations:
 
The model has three variables: two state variables ( and ) and one parameter (). The simulation algorithm is shown in Fig. 7.20.
 
Fig. 7.20: Ejs' simulation algorithm.
 
The model equations are defined in a ODE page of the Evolution panel (see Fig. 7.21).
 
Fig. 7.21: Evolution panel.
 
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View
 
The tree of elements is shown in Fig. 7.22. Open the virtual-lab and look at the properties of the tree elements.
 
Fig. 7.22: Tree of elements.
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