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1. Homoclinic bifurcations: Consider an autonomous system of ordinary differential equations depending on a parameter $$ \tag{a1 } {\dot{x} } = f ( x, \alpha ) , \quad x \in \mathbf R ^ {n} , \alpha \in \mathbf R ^ {1} , $$ where $ f $ is smooth. Denote by $ \varphi _ \alpha ^ {t ... (Mathematics) [100%] 2023-10-12
2. Codimension-two bifurcations: In a generic autonomous system of ordinary differential equations depending upon parameters, $$ \tag{a1} {\dot{x} } = f ( x, \alpha ) , $$ where $ f : {\mathbf R ^ {n} \times \mathbf R ^ {p}} \rightarrow {\mathbf R ^ {n}} $ is smooth, two codimension-one singularities of equilibria ... (Mathematics) [81%] 2023-10-25

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1. Bifurcation: A term in certain branches of mathematics, applied to situations in which some object $ \mathfrak D = \mathfrak D ( \lambda ) $ depends on a parameter $ \lambda $( which is not necessarily scalar) and which is such that in any neighbourhood of a certain ... (Mathematics) [100%] 2023-12-22
2. Bifurcation: A bifurcation of a dynamical system is a qualitative change in its dynamics produced by varying parameters. Consider an autonomous system of ordinary differential equations (ODEs) \[\tag{1} \dot{x}=f(x,\lambda),\ \ \ x \in {\mathbb R}^n, \ \ \ \lambda \in ... [100%] 2021-12-24 [Bifurcations] [Dynamical Systems]...
3. Bautin bifurcation: The Bautin bifurcation is a bifurcation of an equilibrium in a two-parameter family of autonomous ODEs at which the critical equilibrium has a pair of purely imaginary eigenvalues and the first Lyapunov coefficient for the Andronov-Hopf bifucation vanishes ... [70%] 2021-12-24 [Dynamical Systems] [Bifurcations]...
4. Bifurcation (law): Bifurcation is a judge's ability in law to divide a trial into two parts so as to render a judgment on a set of legal issues without looking at all aspects. Frequently, civil cases are bifurcated into separate liability ... (Social) [70%] 2023-11-15
5. Bifurcation diagram: In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to ... (Visualization of sudden behavior changes caused by continuous parameter changes) [70%] 2023-09-18 [Chaos theory] [Bifurcation theory]...
6. Bifurcation locus: In complex dynamics, the bifurcation locus of a parameterized family of one-variable holomorphic functions informally is a locus of those parameterized points for which the dynamical behavior changes drastically under a small perturbation of the parameter. Thus the bifurcation ... [70%] 2023-12-28 [Complex analysis]
7. Bifurcation lake: A bifurcation lake is a lake that has outflows into two different drainage basins and thus the drainage divide cannot be defined exactly because it is situated in the middle of the lake. Vesijako (the name Vesijako actually means "drainage ... (Earth) [70%] 2024-04-05 [Hydrology] [Geomorphology]...