Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
bifurcation theory concept
|
| gptkbp:appliesTo |
ordinary differential equations
continuous-time dynamical systems |
| gptkbp:describes |
local bifurcation in which a fixed point of a dynamical system loses stability
|
| gptkbp:field |
gptkb:mathematics
dynamical systems nonlinear dynamics |
| gptkbp:firstDescribed |
1942
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hopf bifurcation
|
| gptkbp:namedAfter |
gptkb:Eberhard_Hopf
|
| gptkbp:occurredIn |
pair of complex conjugate eigenvalues of the linearization cross the imaginary axis
|
| gptkbp:relatedTo |
gptkb:Poincaré–Bendixson_theorem
gptkb:Andronov–Hopf_bifurcation bifurcation theory limit cycle nonlinear oscillations |
| gptkbp:result |
emergence of a periodic solution (limit cycle)
|
| gptkbp:type |
gptkb:subcritical_Hopf_bifurcation
gptkb:supercritical_Hopf_bifurcation |
| gptkbp:usedIn |
biology
chemistry ecology economics engineering neuroscience physics |
| gptkbp:bfsParent |
gptkb:Dynamical_Systems
|
| gptkbp:bfsLayer |
5
|