Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
discrete dynamical system |
| gptkbp:category |
iterated map
nonlinear map one-dimensional map |
| gptkbp:citation |
Robert May, 1976, "Simple mathematical models with very complicated dynamics"
|
| gptkbp:definedIn |
x_{n+1} = r x_n (1 - x_n)
|
| gptkbp:domain |
0 < x_n < 1
|
| gptkbp:exhibits |
deterministic chaos
sensitive dependence on initial conditions chaotic behavior fixed points periodic orbits |
| gptkbp:field |
gptkb:mathematics
chaos theory dynamical systems |
| gptkbp:has_attractor |
strange attractor
|
| gptkbp:has_fixed_point |
x = 0
x = 1 - 1/r |
| gptkbp:hasApplication |
complex systems
ecology economics physics |
| https://www.w3.org/2000/01/rdf-schema#label |
Logistic map
|
| gptkbp:introduced |
gptkb:Pierre_François_Verhulst
|
| gptkbp:introducedIn |
1845
|
| gptkbp:notableFor |
universality
self-similarity fractal structure route to chaos simple equation with complex behavior |
| gptkbp:parameter |
r
|
| gptkbp:parameter_range |
0 < r < 4
|
| gptkbp:relatedTo |
gptkb:quadratic_map
gptkb:Feigenbaum_constant tent map Lyapunov exponent bifurcation diagram |
| gptkbp:shows_chaos_for |
r > 3.57
|
| gptkbp:shows_period_doubling_for |
3 < r < 3.57
|
| gptkbp:studiedBy |
chaos
bifurcation period doubling |
| gptkbp:used_in |
mathematical biology
population dynamics |
| gptkbp:variant |
x_n
|
| gptkbp:visualizes |
gptkb:cobweb_plot
bifurcation diagram |
| gptkbp:bfsParent |
gptkb:Ordinary_Differential_Equations
|
| gptkbp:bfsLayer |
6
|