Global asymptotic properties for a Leslie-Gower food chain model

We study global asymptotic properties of a continuous time Leslie-Gower food chain model. We construct a Lyapunov function which enables us to establish global asymptotic stability of the unique coexisting equilibrium state.Comment: 5 Pages, 1 figure. Keywords: Leslie-Gower model, Lyapunov function, global stabilit

Review on carbonation study of reinforcement concrete incorporating with bacteria as self-healing approach

This study carried out a comprehensive review to determine the carbonation process that causes the most deterioration and destruction of concrete. The carbonation mechanism involved using carbon dioxide (CO2 ) to penetrate the concrete pore system into the atmosphere and reduce the alkalinity by decreasing the pH level around the reinforcement and initiation of the corrosion process. The use of bacteria in the concrete was to increase the pH of the concrete by producing urease enzyme. This technique may help to maintain concrete alkalinity in high levels, even when the carbonation process occurs, because the CO2 accelerates to the concrete and then converts directly to calcium carbonate, CaCO3 . Consequently, the self-healing of the cracks and the pores occurred as a result of the carbonation process and bacteria enzyme reaction. As a result of these reactions, the concrete steel is protected, and the concrete properties and durability may improve. However, there are several factors that control carbonation which have been grouped into internal and external factors. Many studies on carbonation have been carried out to explore the effect of bacteria to improve durability and concrete strength. However, an in-depth literature review revealed that the use of bacteria as a self-healing mechanism can still be improved upon. This review aimed to highlight and discuss the possibility of applying bacteria in concrete to improve reinforcement concrete

Stability and Hopf Bifurcation in a Three-Species Food Chain System With Harvesting and Two Delays

In this paper, we analyze the dynamics of a delayed food chain system with harvesting. Sufficient conditions for the local stability of the positive equilibrium and for the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation. Formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis

Permanence and periodic solution for a modified Leslie-Gower type predator-prey model with diffusion and non constant coefficients

In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results

On the dynamics of a class of multi-group models for vector-borne diseases

The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number $\mathcal{R}_0$ and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium---usually termed the endemic equilibrium (EE)---that exists if, and only if, $\mathcal{R}_0>1$. We also show that, if $\mathcal{R}_0\leq1$, then the DFE equilibrium is globally asymptotically stable, while when $\mathcal{R}_0>1$, we have that the EE is globally asymptotically stable

On the Lyapunov functional of Leslie-Gower predator-prey models with time-delay and Holling's functional responses

The global stability on the dynamical behavior of the Leslie-Gower predator-prey system with delayed prey specific growth is analyzed by constructing the corresponding Lyapunov functional. Three different types of famous Holling's functional responses are considered in the present study. The sufficient conditions for the global stability analysis of the unique positive equilibrium point are derived accordingly. A numerical example is presented to illustrate the effect of different Holling-Type functional responses on the global stability of the Leislie-Gower predator-prey model

On a diffusive predator-prey model with nonlinear harvesting

Abstract In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns

Persistence and Stability for a Generalized Leslie-Gower Model with Stage Structure and Dispersal

A generalized version of the Leslie-Gower predator-prey model that incorporates the prey structure and predator dispersal in two-patch environments is introduced. The focus is on the study of the boundedness of solution, permanence, and extinction of the model. Sufficient conditions for global asymptotic stability of the positive equilibrium are derived by constructing a Lyapunov functional. Numerical simulations are also presented to illustrate our main results

Dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey

In this paper, the dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie-Gower predator-prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie-Gower predator-prey system such as two saddle-node bifurcations and one Bogdanov-Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.Comment: 20 pages, 10 figure