{{{id=1| ##################### ###### Code Starts ## ##################### ##################### #Bifurcation Diagram 2D #by Sinan Kapcak #2017 ##################### a,x,y=var('a x y') @interact def _( f=input_box(label='$f(x,y)=$',default=a*y/(x^2 + y+1),width=60), g=input_box(label='$g(x,y)=$',default=x/(y^2 + x+1),width=60), P0=input_box(default=( n(.6,digits=3),n(.2,digits=3 )),label='$(x_0,y_0)$',width=35), parameter=input_box(default=(0,4),label='Interval for $a$',width=35),#,auto_update=False iterasyon=input_box(default=200,label='Quality Parameter#1',width=12),#number of iterations: 400 is good subint=input_box(default=200,label='Quality Parameter#2',width=12),#number of subinterval: 500 is good figs=slider(2, 20, 1, default=6,label='Figure size'), ar=slider([2^n for n in [-10..10]], default=1,label='Aspect Ratio' ) ): paramin=parameter[0] paramax=parameter[1] kk=(paramax-paramin)/subint paralist=[paramin+i*kk for i in range(1+subint) ] biflistx=[] biflisty=[] for j in range(len(paralist)): nok=[(P0[0],P0[1] )]#list of points for i in range(iterasyon): nok.append((f(x=nok[i][0],y=nok[i][1],a=paralist[j] ),g(x=nok[i][0],y=nok[i][1],a=paralist[j]))) nok_x=[ nok[-m][0] for m in [1..(iterasyon*2/5)] ] nok_y=[ nok[-m][1] for m in [1..(iterasyon*2/5)] ] for mm in range(len(nok_x)): biflistx.append( [paralist[j] ,nok_x[mm]]) biflisty.append( [paralist[j] ,nok_y[mm]]) biflistgrafx=list_plot(biflistx, plotjoined=False, color='grey',alpha=.3,pointsize=1) biflistgrafy=list_plot(biflisty, plotjoined=False, color='red',alpha=.3,pointsize=1) graf=biflistgrafx+biflistgrafy show(graf,frame=False,axes=True,axes_labels=['$a$','$x_n,y_n$'],figsize=figs,aspect_ratio=ar) ##################### ###### Code Ends #### ##################### ///

$f(x,y)=$

$g(x,y)=$

$(x_0,y_0)$

Interval for $a$

Quality Parameter#1

Quality Parameter#2

Figure size

Aspect Ratio

}}} {{{id=2| /// }}}