arXiv subjects
Publications and source records attributed to M. R. Razvan.
This paper is concerned with index pairs in the sense of Conley index theory for flows relative to pseudo-gradient vector fields for $C^1$-functions satisfying Palais-Smale condition. We prove a deformation theorem for such index pairs to obtain a Lusternik-Schnirelmann type result in Conley index theory.
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 field to be an isolated invariant set. As a result we show the existence of infinitely many homoclinic orbits for a critical point with the Poincare index greater than one.
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 respectively govern the existence and stability of an endemic proportion equilibrium, the increase of the total population and the growth of the infective population. This paper gereralize the results of Busenberg and van den Driessche.
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 need not be unique.
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 on the discussion of the existence and stability of equilibria of the proportions system and the result is in terms of a threshold parameter which governs the stability of the disease free equilibrium.
Let $ϕ^t$ be a continuous flow on a metric space $X$ and $I$ be an isolated invariant set with an index pair $(N,L)$ and a Morse decomposition $\{M_i\}^n_{i=1}$. For every category $ν$ on $N/L$, we prove that $ν(N/L)\leq ν([L])+\sum_{i=1}^n ν(M_i)$. As a result if $ϕ^t|_I$ is gradient-like and $X$ is semi-locally contractible, then $ϕ^t$ has at least $ν_H(h(I))-1$ rest points in $I$ where $h(I)$ is the Conley index of $I$ and $ν_H$ is the Homotopy Lusternik-Schnirelmann category.
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 decomposition.
This paper is concerned with some well-known Ljusternik-Schnirelmann categories. We desire to find some links and relations among them. This has been done by using the concepts of precategoty, T-collection and closure of a category.