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A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely… (More)

- Carmen Chicone
- Encyclopedia of Complexity and Systems Science
- 2009

- C. CHICONE
- 1995

The long term perturbation of a Newtonian binary system by an incident gravitational wave is discussed in connection with the issue of gravitational ionization. The periodic orbits of the planar tidal equation are investigated and the conditions for their existence are presented. The possibility of ionization of a Keplerian orbit via gravitational radiation… (More)

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.

- C. Chicone, D. G. Retzloff
- 1996

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the KolmogorovArnold-Moser theory to the question of gravitational ionization is… (More)

- C. Chicone, D. G. Retzloff
- 1996

The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold… (More)

- James D Benson, Carmen C Chicone, John K Critser
- Journal of mathematical biology
- 2011

Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general nondimensional model was introduced that encompassed solute and solvent transmembrane flux for a wide variety of solutes and flux mechanisms. Moreover, in many biological applications it is of considerable… (More)

- TOKA DIAGANA, GASTON NGUEREKATA, Carmen C. Chicone, NGUYEN VAN MINH
- 2004

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form (∗) u̇(t) = Au(t) + f(t), where A generates a holomorphic semigroup and f is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying… (More)

- C. Chicone
- 2002

The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation… (More)

- Carmen Chicone, Weishi Liu
- SIAM J. Math. Analysis
- 2000

Abstract A persistence theorem for attracting invariant tori for systems subjected to rapidly oscillating perturbations is proved The singular nature of these perturbations prevents the direct application of the standard persistence results for normally hyperbolic invariant manifolds However as is illustrated in this paper the theory of normally hyperbolic… (More)