In this paper, we study a three-dimensional predator-prey model consisting of two communicating prey patches and a predator population associated with a central habitat. Predation uses Holling type II predation functional response, and environmental fluctuations combine a common Brownian component with independent residual components. We establish existence and uniqueness of global solutions, positivity for strictly positive initial states, and uniform moment bounds of every positive order. A sufficient persistence criterion is formulated using two boundary growth rates: the prey recovery rate at extinction and the predator invasion rate in the stationary predator-free environment.
In this paper, the Jensen's inequality for harmonically convex functions is established. Some refinements of Hermite-Hadamard inequality for harmonically convex functions are also obtained.
This paper develops a time-inhomogeneous Ito diffusion population model subject to multiplicative random catastrophes. Closed-form transient moments of arbitrary integer order are derived. For a homogeneous benchmark, the expected-population exponent depends on E[Y], whereas the almost-sure sample-path exponent depends on E[log Y] and the diffusion correction. This creates a parameter region in which the expected population grows while typical sample paths decline exponentially. A nonnegative mean-path gap is obtained from log y <= y-1. Random catastrophe severity and seasonal environments are also considered. Monte Carlo experiments illustrate that a rising ensemble mean can coexist with a sharply declining median population.
In this paper, we first establish that every operator $ T \in B_{n}(\Omega)$ is frequently hypercyclic. Second, we show that the inverse $T^{-1}$ of such operators is also frequently hypercyclic when $T$ satisfies mild spectral conditions (e.g., its spectrum excludes the origin). Third, we characterize the frequent hypercyclicity of operators in the commutant of $T \in B_{n}(\Omega)$ different from $\lambda I$. This work advances the theory of frequent hypercyclicity by establishing a unified framework for operators in $B_{n}(\Omega)$, their inverses, and their multiples, thus complementing the incomplete studies in literature.
Introduction: Although Burundi and Rwanda have similarities in socio-cultural terms, the countries show different paths in terms of family planning and fertility reduction. Objective: The present study aims to compare the determinants of the use of modern contraceptive methods among women in union in these two countries. Methodology: To this end, the researchers used data from the Demographic and Health Surveys (DHS) which have already been carried out in the two countries. The analysis was carried out using stepwise binary logistic regression, and enabled the researchers to identify and prioritize the determinants of the use of modern contraceptive methods for both countries. Results: The results show that age, number of living children, ideal number of children, place of residence, region of residence, religion, woman's level of education and employment sector are common determinants for both countries. However, it should be noted that, unlike in Burundi, the number of living children, place of residence and religion are no longer determining factors in Rwanda. Conclusion: To enable Burundi to progress with its family planning policy, it is important to raise awareness of the advantages of a smaller family, promote education for all and facilitate women's access to employment.
