Counting roots of the characteristic equation for linear delay-differential systems

[摘要] A formula is given that counts the number of roots in the positive half plane of the characteristic equation for general real constant coefficient, linear delay-differential systems. The formula is used to establish necessary and sufficient conditions for asymptotic stability of the zero solution of linear delay-differential systems. The formula is potentially useful in verifying stability hypotheses that arise in bifurcation analysis of autonomous delay-differential system. Application of the formula to Hopf bifurcation theory for delay-differential systems is discussed, and an example application to an equation with two delays is given. (C) 1997 Academic Press.

[发布日期] 1997-05-20