更改

历史上，经济学家最早给出了U矩阵（也称为Leontief矩阵）的定义，请参照[[投入产出分析]]。后来生态学家Finn将这种分析方法引入到<ref name="finn"/>了生态流网络中用于分析能量流网络。Patten、Ulanowicz等人将这套方法系统化，提出了Environ理论<ref name="environ">{{cite journal | last = Patten| first = Bernard C.| date = 1982 | title = Environs: Relativistic elementary particles for ecology| journal = The American Naturalist| volume = 119| pages =  179-219}}</ref><ref>{{cite journal | last = Patten| first = Bernard C.| date = 1985 | title = Energy Cycling in the Ecosystem| journal = Ecological Modelling| volume = 28| pages =1-71}}</ref><ref>{{cite journal | last = Ulanowicz| first = Roberte E.| last2= Wolff | first2=Wilfried F.| date = 1990 | title = Ecosystem Flow Networks: Loaded Dice?| journal = Mathematical Biosciences| volume = 103| pages =45-68}}</ref>。随后，这些人又将这套方法进一步扩展以讨论能量流的循环与存储问题<ref>{{cite journal | last = Patten| first =  Bernard C.| last2= Higashi| first2=Masahiko| last3= Burns | first2=Thomas P.| date = 1990 | title = Trophic Dynamics in Ecosystem Networks: Significance of Cycles and Storage| journal = Ecological Modelling| volume = 51| pages =41-28}}</ref>以及能量流的节律等问题<ref>{{cite journal | last2 = Burns| first2 =  Thomas P.| last= Higashi| first=Masahiko| last3= Patten| first2=Bernard C.| date = 1993 | title = Network trophic dynamics: the tempo of energy movement and availability in ecosystems| journal = Ecological Modelling| volume = 66| pages =43-64}}</ref>。

历史上，经济学家最早给出了U矩阵（也称为Leontief矩阵）的定义，请参照[[投入产出分析]]。后来生态学家Finn将这种分析方法引入到<ref name="finn"/>了生态流网络中用于分析能量流网络。Patten、Ulanowicz等人将这套方法系统化，提出了Environ理论<ref name="environ">{{cite journal | last = Patten| first = Bernard C.| date = 1982 | title = Environs: Relativistic elementary particles for ecology| journal = The American Naturalist| volume = 119| pages =  179-219}}</ref><ref>{{cite journal | last = Patten| first = Bernard C.| date = 1985 | title = Energy Cycling in the Ecosystem| journal = Ecological Modelling| volume = 28| pages =1-71}}</ref><ref>{{cite journal | last = Ulanowicz| first = Roberte E.| last2= Wolff | first2=Wilfried F.| date = 1990 | title = Ecosystem Flow Networks: Loaded Dice?| journal = Mathematical Biosciences| volume = 103| pages =45-68}}</ref>。随后，这些人又将这套方法进一步扩展以讨论能量流的循环与存储问题<ref>{{cite journal | last = Patten| first =  Bernard C.| last2= Higashi| first2=Masahiko| last3= Burns | first2=Thomas P.| date = 1990 | title = Trophic Dynamics in Ecosystem Networks: Significance of Cycles and Storage| journal = Ecological Modelling| volume = 51| pages =41-28}}</ref>以及能量流的节律等问题<ref>{{cite journal | last2 = Burns| first2 =  Thomas P.| last= Higashi| first=Masahiko| last3= Patten| first2=Bernard C.| date = 1993 | title = Network trophic dynamics: the tempo of energy movement and availability in ecosystems| journal = Ecological Modelling| volume = 66| pages =43-64}}</ref>。

将流网络建模成马尔科夫链不仅仅可以讨论流量、时间等问题，还可以讨论如电导经过某点中转的平均首达时间等问题。<ref>{{cite journal | last = Hilfer| first =  R.| last1= Blumen| first=A.| date = 1988| title = Probabilistic interpretation of the Einstein relation| journal = Physical Review A| volume = 37| pages =578-581}}</ref>

将流网络建模成马尔科夫链不仅仅可以讨论流量、时间等问题，还可以讨论如电导经过某点中转的平均首达时间等问题。<ref name="Einstein">{{cite journal | last = Hilfer| first =  R.| last2= Blumen| first2=A.| date = 1988| title = Probabilistic interpretation of the Einstein relation| journal = Physical Review A| volume = 37| pages =578-581}}</ref>

<references/>

<references/>