Systems of first-order chemical reactions (Q1116923)

A reaction system where every species of a finite number of species reacts by first order to every other species is investigated. The convergence behaviour of the solution of the corresponding initial value problem \(dx/dt=Kx\), where x stands for the vector of concentrations and K is the matrix that results from the rate constants, is studied in respect to properties of K that reflect special forms of reaction schemes. In particular, the significance of the principle of microscopic reversibility for the non-existence of oscillatory solutions is pointed out.