An analysis approach to permanence of a delay differential equations model of microorganism flocculation

<p style='text-indent:20px;'>In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.</p>

Identifying Significant Personal and Program Factors that Predict Online EdD Students’ Program Integration

Based on a synthesis of persistence theory and the empirical literature, an online doctoral program integration model was developed using data from 232 online EdD students. A predictive, correlation design and regression analysis were used to examine if personal factors (sex, race, age, marital status, and presence of children in the home) and program factors (stage in doctoral journey, synchronous interactions, cohorts, and orientations) could predict program integration. The entire model was significant. The variables of sex, race, participation in a cohort, and engagement in synchronous communication individually contributed to the variance in program integration.

Dynamical Behaviors of a Pest Epidemic Model with Impulsive Control Over a Patchy Environment

An epidemic model for pest management with impulsive control over a patchy environment is proposed in this paper. We investigate the dynamical behaviors on extinction and permanence and obtain the threshold value [Formula: see text] of dynamics for the impulsive system by utilizing a small amplitude perturbation method, matrix spectral analysis and persistence theory. We prove that the periodic pest-eradication solution of the system is globally asymptotically stable if [Formula: see text], while the system is persistent if [Formula: see text]. Furthermore, by discussion on the two-patch case, we analyze the effects of the dispersal and impulsive control on dynamical behaviors of the system. Some numerical examples are given to illustrate the effectiveness of the obtained results and to demonstrate the complexity such as chaotic characteristic of the system.

The shape of a defense-growth trade-off governs seasonal trait dynamics in natural phytoplankton

Functional trait compositions of communities can adapt to altered environmental conditions ensuring community persistence. Theory predicts that the shape of trade-offs between traits crucially affects these trait dynamics, but its empirical verification from the field is missing. Here, we show how the shape of a defense-growth trade-off governs seasonal trait dynamics of a natural community, using high-frequency, long-term measurements of phytoplankton from Lake Constance. As expected from the lab-derived concave trade-off curve, we observed an alternating dominance of several fast-growing species with intermediate defense levels and gradual changes of the biomass-trait distribution due to seasonally changing grazing pressure. By combining data and modelling, we obtain mechanistic insights on the underlying fitness landscape, and show that low fitness differences can maintain trait variation along the trade-off curve. We provide firm evidence for a frequently assumed trade-off and conclude that quantifying its shape allows to understand environmentally driven trait changes within communities.

Using the Motivational Aspects of Productive Persistence Theory and Social Media Motivators to Improve the ELA Flipped Classroom Experience

This chapter discusses the need to expand upon the pedagogical components of the flipped classroom model to include what is known about motivation as it relates to Productive Persistence Theory (PPT) and social media (SM) in order to increase student success in the English language arts. Motivational incentives suggested, in part, by the PPT literature, are identified and organized by its three non-cognitive aspects of grit, growth mindsets, and belonging. Motivators for SM use are identified in the literature and categorized as seeking, expressing, and engaging. Implications drawn are that student learning is personal, developmental, and social, all operating simultaneously. Also, that this multidimensionality is involved in motivating each individual student and that SM inherently supports such motivation. A conceptual framework is presented that demonstrates how both PPT and SM allow teachers to meet students where they are in their learning and in their personal and social growth and development.

Using the Motivational Aspects of Productive Persistence Theory and Social Media Motivators to Improve the ELA Flipped Classroom Experience

This chapter discusses the need to expand upon the pedagogical components of the flipped classroom model to include what is known about motivation as it relates to Productive Persistence Theory (PPT) and social media (SM) in order to increase student success in the English language arts. Motivational incentives suggested, in part, by the PPT literature, are identified and organized by its three non-cognitive aspects of grit, growth mindsets, and belonging. Motivators for SM use are identified in the literature and categorized as seeking, expressing, and engaging. Implications drawn are that student learning is personal, developmental, and social, all operating simultaneously. Also, that this multidimensionality is involved in motivating each individual student and that SM inherently supports such motivation. A conceptual framework is presented that demonstrates how both PPT and SM allow teachers to meet students where they are in their learning and in their personal and social growth and development.

DYNAMICS OF COMPETING STRAINS WITH SATURATED INFECTIVITY AND MUTATION ON NETWORKS

This paper deals with the dynamical behavior of a two-strain epidemic model in a complex network with saturated infectivity and mutation. The model is shown to exhibit the phenomena of strain coexistence where two epidemic strains co-exist and strain replacement where the strain with smaller basic reproduction number can become predominant. By using the stability and persistence theory of dynamical systems, we calculate the epidemic threshold, and show that above which at least one strain persists in a population, and also obtain the critical values to discriminate the strain coexistence and replacement. The results suggest that the newly mutated strain can spread in the population, even if it has a very small transmissivity.

Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure

A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.