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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:discrete_dynamical_system
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gptkbp:category
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iterated map
nonlinear map
one-dimensional map
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gptkbp:citation
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Robert May, 1976, "Simple mathematical models with very complicated dynamics"
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gptkbp:definedIn
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x_{n+1} = r x_n (1 - x_n)
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gptkbp:domain
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0 < x_n < 1
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gptkbp:exhibits
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deterministic chaos
sensitive dependence on initial conditions
chaotic behavior
fixed points
periodic orbits
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gptkbp:field
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gptkb:mathematics
chaos theory
dynamical systems
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gptkbp:has_attractor
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gptkb:strange_attractor
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gptkbp:has_fixed_point
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x = 0
x = 1 - 1/r
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gptkbp:hasApplication
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complex systems
ecology
economics
physics
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gptkbp:introduced
|
gptkb:Pierre_François_Verhulst
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gptkbp:introducedIn
|
1845
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gptkbp:notableFor
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universality
self-similarity
fractal structure
route to chaos
simple equation with complex behavior
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gptkbp:parameter
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r
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gptkbp:parameter_range
|
0 < r < 4
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gptkbp:relatedTo
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gptkb:quadratic_map
gptkb:Feigenbaum_constant
tent map
Lyapunov exponent
bifurcation diagram
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gptkbp:shows_chaos_for
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r > 3.57
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gptkbp:shows_period_doubling_for
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3 < r < 3.57
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gptkbp:studiedBy
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gptkb:bifurcation
chaos
period doubling
|
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gptkbp:used_in
|
mathematical biology
population dynamics
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gptkbp:variant
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x_n
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gptkbp:visualizes
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gptkb:cobweb_plot
bifurcation diagram
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gptkbp:bfsParent
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gptkb:Ordinary_Differential_Equations
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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Logistic map
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