Bifurcations in first-order ODEs

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorVick, Brian-
Data de aceite: dc.date.accessioned2019-08-21T19:30:23Z-
Data de disponibilização: dc.date.available2019-08-21T19:30:23Z-
Data de envio: dc.date.issued2009-
Data de envio: dc.date.issued2009-09-29-
Data de envio: dc.date.issued2013-03-14-
Data de envio: dc.date.issued2013-03-14-
Data de envio: dc.date.issued2013-03-14-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/22713-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/493507-
Descrição: dc.descriptionEducação Superior::Ciências Exatas e da Terra::Matemática-
Descrição: dc.descriptionA first-order autonomous ordinary differential equation (ODE) with a parameter r has the general form dx/dt = f(x,r). The fixed points are the values of x for which f(x,r)=0. A bifurcation occurs when the number or the stability of the fixed points changes as system parameters change. The classical types of bifurcations that occur in nonlinear dynamical systems are produced from the following prototypical differential equations: saddle: dx/dt=r+x²; transcritical: dx/dt=rx-x²; supercritical pitchfork: dx/dt=rx-x³; subcritical pitchfork:rx+x³. This Demonstration shows bifurcations of these nonlinear first-order ODEs as you vary the parameter r. The top figure shows the phase portrait, dx/dt versus x, with stable fixed points indicated by solid disks and unstable fixed points as open circles. The bottom figure shows the solutions, x(t) versus t, starting from a number of initial states with stable fixed points indicated by solid lines and unstable fixed points as dashed lines. You can vary both the number of initial states and time duration, tmax. Note how the fixed points and solutions change as bifurcations occur as you vary the parameter r-
Idioma: dc.languageen-
Publicador: dc.publisherWolfram Demonstrations Project-
Relação: dc.relationBifurcationsInFirstOrderODEs.nbp-
Direitos: dc.rightsDemonstration freeware using MathematicaPlayer-
???dc.source???: dc.sourcehttp://demonstrations.wolfram.com/topic.html?topic=Dynamical+Systems+Theory&limit=20-
Palavras-chave: dc.subjectSistemas dinâmicos-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Sistemas Dinâmicos-
Título: dc.titleBifurcations in first-order ODEs-
???dc.description2???: dc.description2Mostrar bifurcações das equações diferenciais ordinárias não-lineares, quando varia-se o parâmetro r-
???dc.description3???: dc.description3This demonstration needs the "MathematicaPlayer.exe" to run. Find it in http://objetoseducacionais2.mec.gov.br/handle/mec/4737-
Aparece nas coleções:Repositório Institucional - MEC BIOE

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