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| goto [:interact:interact main page] [[TableOfContents]] |
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| {{{ | {{{#!sagecell |
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| ''' Returns a graphics object of a plot of the function and a cobweb trajectory starting from the value start. INPUT: a_function: a function of one variable start: the starting value of the iteration mask: (optional) the number of initial iterates to ignore iterations: (optional) the number of iterations to draw, following the masked iterations xmin: (optional) the lower end of the plotted interval xmax: (optional) the upper end of the plotted interval EXAMPLES: sage: f = lambda x: 3.9*x*(1-x) sage: show(cobweb(f,.01,iterations=200), xmin = 0, xmax = 1, ymin=0) ''' basic_plot = plot(a_function, xmin = xmin, xmax = xmax) id_plot = plot(lambda x: x, xmin = xmin, xmax = xmax) iter_list = [] current = start for i in range(mask): current = a_function(current) for i in range(iterations): iter_list.append([current,a_function(current)]) current = a_function(current) iter_list.append([current,current]) cobweb = line(iter_list, rgbcolor = (1,0,0)) return basic_plot + id_plot + cobweb |
''' Returns a graphics object of a plot of the function and a cobweb trajectory starting from the value start. INPUT: a_function: a function of one variable start: the starting value of the iteration mask: (optional) the number of initial iterates to ignore iterations: (optional) the number of iterations to draw, following the masked iterations xmin: (optional) the lower end of the plotted interval xmax: (optional) the upper end of the plotted interval EXAMPLES: sage: f = lambda x: 3.9*x*(1-x) sage: show(cobweb(f,.01,iterations=200), xmin = 0, xmax = 1, ymin=0) ''' basic_plot = plot(a_function, xmin = xmin, xmax = xmax) id_plot = plot(lambda x: x, xmin = xmin, xmax = xmax) iter_list = [] current = start for i in range(mask): current = a_function(current) for i in range(iterations): iter_list.append([current,a_function(current)]) current = a_function(current) iter_list.append([current,current]) cobweb = line(iter_list, rgbcolor = (1,0,0)) return basic_plot + id_plot + cobweb |
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| def f(x): return eval(f_text) show(cobweb(f, start_val, iterations = its)) |
def f(x): return eval(f_text) show(cobweb(f, start_val, iterations = its)) |
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| {{attachment:cobweb.png}} == Cythonized Logistic Orbit Map == By Marshall Hampton {{{ %cython cpdef double logorb(double k,long N,double x0): cdef double x = x0 cdef long i for i from 1 <= i <= N: x = k*x*(1-x) return x cpdef logtraj(double k,long N, double x0): cdef double x = x0 xvals = [] cdef long i for i from 1 <= i <= N: x = k*x*(1-x) xvals.append(x) return xvals }}} {{{#!sagecell html('<h2>Orbit diagram of the logistic map</h2>') @interact def logistic_bifs(k_min = slider(0.0,4.0,.001,3.5), k_max = slider(0.0,4.0,.001,4.0)): tkmax = max(k_min, k_max) tkmin = min(k_min, k_max) dk = (tkmax - tkmin)/1000.0 xpts = [] x = .5 for k in srange(tkmin,tkmax,dk): x = logorb(k,100,x) ks = logtraj(k,12,x) if max(ks)-min(ks) < .001: xpts.append([k,x]) else: x = logorb(k,1000,x) ks = logtraj(k,100,x) xpts = xpts + [[k,q] for q in ks] show(points(xpts, pointsize = 1), figsize = [6,6]) }}} {{attachment:logisticorbits.png}} |
Sage Interactions - Dynamical Systems
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Contents
Cobweb diagrams on [0,1]
by Marshall Hampton.
Cythonized Logistic Orbit Map
By Marshall Hampton
%cython
cpdef double logorb(double k,long N,double x0):
cdef double x = x0
cdef long i
for i from 1 <= i <= N:
x = k*x*(1-x)
return x
cpdef logtraj(double k,long N, double x0):
cdef double x = x0
xvals = []
cdef long i
for i from 1 <= i <= N:
x = k*x*(1-x)
xvals.append(x)
return xvals
