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第25行：
第25行： − + − [[File:Chaosorderchaos.png|300px|right|thumb|Period-halving bifurcations (L) leading to order, followed by period doubling bifurcations (R) leading to chaos.]] − Period-halving bifurcations (L) leading to order, followed by period doubling bifurcations (R) leading to chaos.+ − 周期分岔(l)导致有序，周期倍增分岔(r)导致混沌。 第130行：
第128行： − −
→Local bifurcations
*全局分岔Global bifurcations是指不能仅通过平衡点(或不动点)的稳定性来分析的分岔，它常在系统的较大不变集之间“碰撞”时，或较大不变集与系统的平衡点“碰撞”时出现。
*全局分岔Global bifurcations是指不能仅通过平衡点(或不动点)的稳定性来分析的分岔，它常在系统的较大不变集之间“碰撞”时，或较大不变集与系统的平衡点“碰撞”时出现。
===Local bifurcations===
===局部分岔Local bifurcations===
[[File:Chaosorderchaos.png|300px|right|thumb|周期减半分岔(L)导致有序，周期倍增分岔(R)导致混沌.]]
A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems (those described by maps rather than ODEs), this corresponds to a fixed point having a [[Floquet multiplier]] with modulus equal to one. In both cases, the equilibrium is ''non-hyperbolic'' at the bifurcation point.
A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems (those described by maps rather than ODEs), this corresponds to a fixed point having a [[Floquet multiplier]] with modulus equal to one. In both cases, the equilibrium is ''non-hyperbolic'' at the bifurcation point.
* [[Neimark–Sacker bifurcation|Neimark–Sacker]] (secondary Hopf) bifurcation
* [[Neimark–Sacker bifurcation|Neimark–Sacker]] (secondary Hopf) bifurcation
===Global bifurcations===
===Global bifurcations===