Estimates of Zones where All Solutions of Functional Equations Change their Signs

The studied linear discrete-continuous system contains two coupled subsystems: one with continuous-time dynamics, the other with discrete-time dynamics. Continuoustime dynamics are described by ordinary linear differential equations, whereas discretetime dynamics are described by difference equations for the system state jumps at prescribed time instants. Systems of three following degrees of generality are considered: time-varying, time-periodical and time-constant discrete-continuous systems. Some significant observability properties of such systems are presented. Kalman – like observability criteria are proposed for each of these classes of systems. Hautus-like eigenvalues observability criteria are developed for time-constant models. Discrete-continuous observer design method is developed. The method based on proposed solution of an eigenvalue assignment problem for a discrete-continuous constant parameters system. Predator prey dynamics in a uniform medium lead to directed percolation and wave train propagation Alexandra Agranovich 1 , Yoram Louzoun 1 Department of Mathematics and Gonda Brain Research Center, Bar Ilan University, Ramat Gan 52900, Israel