Effect of randomly fluctuating environment on autotroph-herbivore model system.
Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach....
Existence of positive periodic solutions to -species nonautonomous food chains with harvesting terms.
Existence of limit cycles in a predator-prey system with a functional response.
Existence of positive periodic solutions of an SEIR model with periodic coefficients
An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.
Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation.
Expansion for the superheating field in a semi-infinite film in the weak- limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak- limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers...
Expansion for the superheating field in a semi-infinite film in the weak-κ limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion...
Extinction and permanence of a three-species Lotka-Volterra system with impulsive control strategies.
Extinction in a generalized Lotka-Volterra predator-prey model.
Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances
A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]....