Recurrence plot

<p>In descriptive <a href="/facts/Statistics/DNPsKGYU">statistics</a> and <a href="/facts/Chaos_theory/LTC17vsF">chaos theory</a>, a recurrence plot (RP) is a plot showing, for each moment 
  
    
      
        j
      
    
    {\displaystyle j}
  
 in time, the times at which the state of a <a href="/facts/Dynamical_system/782gREl5">dynamical system</a> returns to the previous state at 
  
    
      
        i
      
    
    {\displaystyle i}
  
,
i.e., when the <a href="/facts/Phase_space/qPe4Fq57">phase space</a> trajectory visits roughly the same area in the phase space as at time 
  
    
      
        j
      
    
    {\displaystyle j}
  
. In other words, it is a plot of
</p>

x
              →
            
          
        
        (
        i
        )
        ≈
        
          
            
              x
              →
            
          
        
        (
        j
        )
        ,
      
    
    {\displaystyle {\vec {x}}(i)\approx {\vec {x}}(j),}

<p>showing 
  
    
      
        i
      
    
    {\displaystyle i}
  
 on a horizontal axis and 
  
    
      
        j
      
    
    {\displaystyle j}
  
 on a vertical axis, where 
  
    
      
        
          
            
              x
              →
            
          
        
      
    
    {\displaystyle {\vec {x}}}
  
 is the state of the system (or its phase space trajectory).
</p>

Recurrence plot open-in-new

Recurrence plot