page_title: Gauss iterated map
section_title: Properties
hierarchical_section_title: Gauss iterated map / Properties
caption_attribution_description: English: Orbit diagram of the iterative gaussian equation for . The red line is a separate equilibrium dependent upon starting conditions -- it is not another cycle (i.e., when the system is not in a two cycle, it is in a one cycle that can be in two positions depending upon starting parameters).
context_page_description: In mathematics, the Gauss map, is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
  where α and β are real parameters.
  Named after Johann Carl Friedrich Gauss, the function maps the bell shaped Gaussian function similar to the logistic map.
context_section_description: In the parameter real space  can be chaotic. The map is also called the mouse map because its bifurcation diagram resembles a mouse (see Figures).
caption: Bifurcation diagram of the Gauss map with 
    
      
        
          α
          =
          6.20
        
      
      {\displaystyle \alpha =6.20}
    
   and 
    
      
        
          β
        
      
      {\displaystyle \beta }
    
   in the range −1 to +1.
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