相对不可约合作系统解的单调性

THE MONOTONE OF SOLUTIONS OF RELATIVELY IRREDUCIBLY COOPERATIVE SYSTEMS

合作系统是一类重要的动力系统 .本世纪八十年代 Hirsch曾就不可约合作系统给出了一系列重要结论 .但在实际问题中有许多合作系统不是不可约的 ,却具有不可约合作系统的性质 .本文提出比不可约性更广的相对不可约概念 ,指出这类系统的解与严格不可约系统的解同样具有强单调性 ,并给出严格的证明 ,从而将 Hirsch的结果做了进一步推广 .

Cooperative system is a kind of important dynamical systems.Hirsch put forward a series of results aboutirreducibly cooperative systems in 1 980 ' s.However,many cooperative systems derived from practical problems,which have the same property as irreducibly cooperative systems,are in fact not irreducible.In this article the concept of relative irreducibility is proposed which is more general than the concept of irreducibility. Moreover,it can be strictly proved that the solutions of relatively irreducibly cooperative systems are strongly monotone like ones of irreducible systems.Then Hirsch' s results are further extended.Finally,a practical example of relatively irreducible blood coagulation systems is introduced.