Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationa
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Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationa
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25بك المحتوى هنا ينقصه الاستشه ...... فإن النظام لا يحتوي على تشعب.
@ar
Bifurcation theory is the math ...... ry points and classified them.
@en
Bifurkacja – zjawisko skokowej ...... edy z kwadratowego na liniowe.
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De wiskundige bifurcatietheori ...... de manieren worden beschreven.
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Eine Bifurkation oder Verzweig ...... ist die logistische Abbildung.
@de
La teoria delle biforcazioni s ...... rso lo studio dei punti fissi.
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La teoría de bifurcaciones es ...... os como en sistemas discretos.
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La théorie des bifurcations, e ...... ans l'organisation du système.
@fr
Теория бифуркаций динамических ...... а (или нескольких параметров).
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分岐（bifurcation）は、力学系においてパラメータの ...... また分岐し…を繰り返すことにより、カオス的振る舞いを見せる。
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25بك المحتوى هنا ينقصه الاستشه ...... فإن النظام لا يحتوي على تشعب.
@ar
Bifurcation theory is the math ...... amed various types of stationa
@en
Bifurkacja – zjawisko skokowej ...... edy z kwadratowego na liniowe.
@pl
De wiskundige bifurcatietheori ...... en oscillaties is van belang.
@nl
Eine Bifurkation oder Verzweig ...... initer Änderung des Parameters
@de
La teoria delle biforcazioni s ...... ioni in due classi principali:
@it
La teoría de bifurcaciones es ...... rtante en ingeniería y física.
@es
La théorie des bifurcations, e ...... ans l'organisation du système.
@fr
Теория бифуркаций динамических ...... а (или нескольких параметров).
@ru
分岐（bifurcation）は、力学系においてパラメータの ...... また分岐し…を繰り返すことにより、カオス的振る舞いを見せる。
@ja
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Bifurcación (matemática)
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Bifurcatietheorie
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Bifurcation theory
@en
Bifurkacja (matematyka)
@pl
Bifurkation (Mathematik)
@de
Teoria delle biforcazioni
@it
Théorie des bifurcations
@fr
Теория бифуркаций
@ru
نظرية التشعب
@ar
分岐 (カオス理論)
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