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gptkbp:instanceOf
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gptkb:mathematical_concept
bifurcation
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gptkbp:alsoKnownAs
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gptkb:tangent_bifurcation
fold bifurcation
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gptkbp:appearsIn
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biology
chemistry
physics
engineering systems
population models
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gptkbp:bifurcationParameter
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r
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gptkbp:category
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local bifurcation
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gptkbp:citation
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gptkb:Strogatz,_Nonlinear_Dynamics_and_Chaos
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gptkbp:codimension
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one
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gptkbp:describes
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collision and annihilation of two fixed points
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gptkbp:exampleEquation
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dx/dt = r + x^2
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gptkbp:field
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gptkb:mathematics
dynamical systems
nonlinear dynamics
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gptkbp:firstDescribed
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gptkb:Henri_Poincaré
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gptkbp:form
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normal form
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gptkbp:hasFixedPoints
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none (after bifurcation)
two (before bifurcation)
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https://www.w3.org/2000/01/rdf-schema#label
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saddle-node bifurcation
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gptkbp:normalFormEquation
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dx/dt = r + x^2
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gptkbp:occurredIn
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a pair of fixed points (one stable, one unstable) merge and disappear
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gptkbp:relatedTo
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gptkb:Hopf_bifurcation
gptkb:transcritical_bifurcation
pitchfork bifurcation
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gptkbp:stabilityChange
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creation or destruction of equilibria
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gptkbp:studiedIn
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ordinary differential equations
discrete dynamical systems
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gptkbp:visualizes
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bifurcation diagram
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gptkbp:bfsParent
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gptkb:Dynamical_Systems
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gptkbp:bfsLayer
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5
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