The changes in the stability of a system of linear differential delay equations resulting from the delay are studied by analyzing the associated eigenvalues of the characteristic equation. A specific contour is mapped by the characteristic equation into the complex plane to give an easy test for stability from an application of the argument principle. When the real part of an eigenvalue is posi...

The purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of Leonhard and Nyquist, can be used to derive simple algorithm to verify stability. This is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study o...

The problem of dispersion of a transferable scalar in a turbulent fluid is considered. The Hopf functional equation for the characteristic functional of the velocity vector and transferable scalar is derived and discussed. The special case of heal conduction with random initial condition is studied in detail. It is shown that the Hopf equation accepts a Gaussian characteristic functional soluti...

It is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is Darboux integrable, then its local Cauchy problem may be solved by ordinary differential equations. In addition, such an equation has infinitely many non-trivial conservation laws. Moreover, Darboux integrable equations have properties in common with infinite dimensional compl...

where ε = μq, ε p q = μp. The systems for which small parameter has a fractional power were studied by V.K. Grigorenko in [1]. The case of the simple roots of the characteristic equations and the case of the equation having only one multiple n root were studied separately. Let us construct the asymptotic solution of the system (1) by the method of perturbed characteristic equation [2] for the c...

A. In [6], M. E. Gurtin and R. C. MacCamy investigated a non-linear agestructured population dynamical model, which served as one of the basic non-linear population dynamical models in the last three decades. They described a characteristic equation but they did not use it to discuss stability of equilibria of the system in certain special cases. In a recent paper [4] M. Farkas deduced a...

If A is a square matrix of order n and I is the unit matrix, the equation in X obtained by equating to zero the determinant \A— \l\ is called the characteristic equation of A. The roots of this equation are called the characteristic roots of A. Although it is not possible to make any definite statement as to the nature of the characteristic roots of the general algebraic matrix A, several autho...

A PID controller is designed for various forms of integrating systems with time delay using direct synthesis method. The method is based on comparing the characteristic equation of the integrating system and PID controller with a filter with the desired characteristic equation. The desired characteristic equation comprises of multiple poles which are placed at the same desired location. The tun...

In this paper we discuss the characteristic equation of a matrix in the maxplus algebra. In their Linear Algebra and Its Applications paper (vol. 101, pp. 87– 108, 1988) Olsder and Roos have used a transformation between the max-plus algebra and linear algebra to show that the Cayley-Hamilton theorem also holds in the max-plus algebra. We show that the derivation of Olsder and Roos is not entir...