Select a map.\nQuadratic, Qc = x*x + c\nQuadratic2, Qc2 = x*x - c\nLogistic, Lc = c*x*(1 - x)\nCubic, Cc = c*x*x*(1 - x)\nCubic2, Cc2 = c*x*(1 - x*x)\nTent, Tc = c*x, -c*x + c\nSine, Sc = c*sin(x)\nSine2, Sc2 = sin(c*x)\nSine3, Sc3 = sin(x/c)\nCosine, Cc = c*cos(x)\nGaussian, Gc = exp(-4.9*x*x) + c\nGausian2, Gc2 = exp(-6.2*x*x) + c\nExponential, Ec = c*x*exp(x)\nHenon, Hc=1+y-c*x*x, y=0.3*x\nVerhulst, Vc=x + c*x*(1 - x)\n
Bifurcation Diagrams or Orbit Diagrams?
What is computed?
A critical point is a point for which the first derivative of the function under examination vanishes; i.e., f'(x) = 0. Said critical point is degenerated if its second derivative also vanishes; i.e., f''(x) = 0. For the quadratic map, f(x) = Qc so f'(x) = 0 and f''(x) = 2. Therefore, x = 0 is a critical point for Qc, and it is nondegenerated. While it is true that seeds no need to be critical points, frequently the most interesting diagrams are obtained with a seed at or nearby a critical point.
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