Delay differential equations are a class of mathematical models describing various natural and engineered phenomena with delayed feedbacks in the system. Mathematical theory of delay differential equations or functional-differential equations have been developed in the second half of twentieth century to study mathematical questions from models of population biology, biochemical reactions, neur...

This paper considers Lur’e type descriptor systems (LDS). The concept of strongly absolute stability is defined for LDS and such a notion is a generalization of absolute stability for Lur’e type standard state-space systems (LSS). A reduced-order LSS is obtained by a standard coordinate transformation and it is shown that the strongly absolute stability of the LDS is equivalent to the absolute ...

Existence and stability of travelling waves are conveniently studied on unbounded domains , for instance, on the real line. Motivated by numerical and experimental studies, we investigate the eeects of truncating the unbounded domain to a large but bounded domain. It is shown that periodic boundary conditions accurately reproduce the L 2-spectrum of the unbounded domain, whereas separated bound...