A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into itself.The phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc fr...A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into itself.The phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=Ax.The structure of the phase space of the FDS(Ln,f)is discussed.The number of limit cycles in the phase space of(Ln,f)is described in Möbius function.The phase spaces of some invertible,nilpotent,and idempotent FDS(Ln,f)are characterized explicitly.展开更多
The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every v...The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every vector in the simplex is a stationary vector.A modification of the characterization is presented in the paper.Some sufficient conditions are derived for any facet of the simplex such that every vector of the facet is a stationary vector.展开更多
基金National Natural Science Foundation of China(Nos.11671258 and 11371086)。
文摘A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into itself.The phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=Ax.The structure of the phase space of the FDS(Ln,f)is discussed.The number of limit cycles in the phase space of(Ln,f)is described in Möbius function.The phase spaces of some invertible,nilpotent,and idempotent FDS(Ln,f)are characterized explicitly.
基金National Natural Science Foundation of China(Nos.1167125811371086)
文摘The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every vector in the simplex is a stationary vector.A modification of the characterization is presented in the paper.Some sufficient conditions are derived for any facet of the simplex such that every vector of the facet is a stationary vector.
