Kinds Of Discrete Systems Research Articles

Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay

A kind of discrete system according to Nicholson's blowflies equation with a finite delay is obtained by the Euler forward method, and the dynamics of this discrete system are investigated. Applying the theory of normal form and center manifold, we not only discuss the linear stability of the equilibrium and the existence of the local Hopf bifurcations, but also give the explicit algorithm for determining the direction of bifurcation and stability of the periodic solution of bifurcation.

Stability criteria in terms of two measures for discrete systems

This paper studies stability problems for two kinds of discrete systems in terms of two different measures. The basic idea of this approach is to discuss the qualitative behaviour of a map h along solutions of discrete systems whose initial value are measured by a second map h 0. By doing this, one may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Stability criteria in terms of two measures are established employing the method of Lyapunov functions and Razumikhin techniques.

Questions of controllability and observability for nonuniformly sampled discrete systems

A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to the arbitrary choice of the sampling instants, is used to improve the sensitivity of system controllability and observability, by exploiting an adequate geometric structure. Some qualitative examples are presented for illustrative purposes.