Stability1D.sagews

%auto
typeset_mode(True, display=False)

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###### Code Starts ##
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#####################
#Stability !D
#by Sinan Kapcak
#2017
#####################


x,y=var('x y')
@interact
def _(
    funct=input_box(label='$f(x)$',default=x-x^2,width=50),
    fipo=input_box(label='Fixed point',default=0,width=50 )):
    if bool(fipo == funct(x=fipo))==False:
            show (LatexExpr(r' x=') , fipo , LatexExpr(r'  \text{ is not a fixed point.}'))
    else:
            if abs( diff(funct,x).substitute(x=fipo))<1:
                show (LatexExpr(r' x^*=') , fipo , LatexExpr(r'  \text{ is an asymptotically stable fixed point.}'))
            if abs( diff(funct,x).substitute(x=fipo))>1:
                show (LatexExpr(r' x^*=') , fipo , LatexExpr(r' \text{ is an unstable fixed point.}'))
            if diff(funct,x).substitute(x=fipo)==1:
                A=0
                n=2
                while A==0:
                    A=diff(funct,x,n).substitute(x=fipo)
                    n=n+1
                if is_odd(n)==True:
                    show (LatexExpr(r' x^*=') , fipo , LatexExpr(r'  \text{ is an unstable (semistable) fixed point.}'))
                else:
                    if A<0:
                        show (LatexExpr(r' x^*=') , fipo , LatexExpr(r' \text{ is an asymptotically stable fixed point.}'))
                    if A>0:
                        show (LatexExpr(r' x^*=') , fipo , LatexExpr(r' \text{ is an unstable fixed point.}' ))
            if diff(funct,x).substitute(x=fipo)==-1:
                funct1=funct(x=funct)
                A=0
                n=2
                while A==0:
                    A=diff(funct1,x,n).substitute(x=fipo)
                    n=n+1
                if A<0:
                    show (LatexExpr(r' x^*=') , fipo , LatexExpr(r' \text{ is an asymptotically stable fixed point.}'))
                if A>0:
                    show (LatexExpr(r' x^*=') , fipo , LatexExpr(r' \text{ is an unstable fixed point.}'))
        
        
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###### Code Ends ####
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Interact: please open in CoCalc