8 papers
On the Poincare Index of Isolated Invariant Sets
M. R. Razvan, M. Fotouhi Firoozabad
In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector fiel…
Multiple Equilibria for an SIRS Epidemiological System
M. R. Razvan
An SIRS type model of disease transmission in an open environment is discussed. We use the Poincaré index together with a perturbation method to show that the endemic proportions n…
Analysis of a Disease Transmission Model with two Groups of Infectives
M. R. Razvan
In this paper, we give a complete analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of infective individuals. It is mainly based o…
Lusternik-Schnirelmann Theory for a Morse Decomposition
M. R. Razvan
Let be a continuous flow on a metric space and be an isolated invariant set with an index pair and a Morse decomposition . For every category…
On Conley's Fundamental Theorem of Dynamical Systems
M. R. Razvan
In this paper, we generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of regular index filtration for every Morse de…
The Dynamics of a Vertically Transmitted Disease
M. R. Razvan
An SIRS epidemiological model for a vertically transmitted disease is discussed. We give a complete global analysis in terms of three explicit threshold parameters which respective…