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The theory of Lyapunov exponents and methods from ergodic theory have been employed by several authors in order to study persistence properties of dynamical systems generated by ODEs or by maps. Here we derive sufficient conditions for uniform persistence, formulated in the language of Lyapunov exponents, for a large class of dissipative discrete-time… (More)

- Paul Leonard Salceanu, Hal L. Smith
- Journal of biological dynamics
- 2009

A discrete-time susceptible and infected (SI) epidemic model, with less than 100% vertical disease transmission, for the spread of a fungal disease in a structured amphibian host population, is analysed. Criteria for persistence of the population as well as the disease are established. Stability results for host extinction and for the disease-free… (More)

- Azmy S. Ackleh, Paul Leonard Salceanu
- Journal of biological dynamics
- 2015

We analyse a discrete-time Ricker competition model with n competing species and give sufficient conditions, which depend on the competition coefficients only, for one species to survive (not necessarily at an equilibrium) and to drive all the other species to extinction. Our results complement and extend similar existing results from the literature. For… (More)

Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of R for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are… (More)

- Azmy S. Ackleh, Paul Leonard Salceanu
- Journal of mathematical biology
- 2014

A nonautonomous version of the SIR epidemic model in Ackleh and Allen (2003) is considered, for competition of [Formula: see text] infection strains in a host population. The model assumes total cross immunity, mass action incidence, density-dependent host mortality and disease-induced mortality. Sufficient conditions for the robust uniform persistence of… (More)

As exemplified by classic Lotka–Volterra theory, there are several canonical outcomes possible to a two species (interference) competitive interaction: coexistence, initial condition-dependent competitive exclusion of one species, or the global exclusion of one species. Evolutionary versions of Lotka–Volterra dynamics have been investigated in order to see… (More)

- Paul Leonard Salceanu
- Mathematical biosciences and engineering : MBE
- 2011

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is… (More)

We consider ecological difference equations of the formX t+1 = X i tAi(Xt) where X t is a vector of densities corresponding to the subpopulations of species i (e.g. subpopulations of different ages or living in different patches), Xt = (X t , X 2 t , . . . , X m t ) is state of the entire community, and Ai(Xt) are matrices determining the update rule for… (More)

- Jude D. Kong, Paul Leonard Salceanu, Hao Wang
- Journal of mathematical biology
- 2017

Biodegradation, the disintegration of organic matter by microorganism, is essential for the cycling of environmental organic matter. Understanding and predicting the dynamics of this biodegradation have increasingly gained attention from the industries and government regulators. Since changes in environmental organic matter are strenuous to measure,… (More)

A discrete-time population model in which individuals are distributed over a discrete phenotypic trait-space is studied. It is shown that, for an irreducible mutation matrix , if mutation is small, then an interior equilibrium exists, that is globally asymptotically stable in , while for arbitrary large mutation each trait persists uniformly. For the model… (More)

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