We consider a stochastic predator prey model with the Bedington -DeAngelis functional response. Firstly, we prove the existence, uniqueness and positivity of solutions. Then, the boundedness of moments of population are studied. Finally, we show the weak convergence of densities of prey to a singular measure in a special case, and give some upper growth and exponential death rates of population...

In this paper, we consider a simple chemostat model involving a single species feeding on redundant substrate with a constant yield term. Many experiments indicate that very high substrate concentrations actually inhibit growth. Instead of assuming the prevalent Monod kinetics for growth rate of cells, we use a non-monotonic functional response function to describe the inhibitory effect. A deta...

A delayed predator-prey model with diffusion and competition is proposed. Some sufficient conditions on uniform persistence of the model have been obtained. By applying LiapunovRazumikhin technique, we will point out, under almost periodic circumstances, a set of sufficient conditions that assure the existence and uniqueness of the positive almost periodic solution which is globally asymptotica...

Keywords: Time delay Global stability Lyapunov functional Nonlinear incidence a b s t r a c t In this paper, a delayed HIV-1 infection model with nonlinear incidence of infection is reinvestigated. It is shown that if the reproduction number R > 1, then the system is permanent , and the infective equilibrium of the system is globally asymptotically stable. Thus, the global dynamics of the syste...

and Applied Analysis 3 2. The Model System Inmodel (1), the productf(u)g(V) gives the rate atwhich prey is consumed. The prey consumed per predator, f(u)g(V)/V, was termed as the functional response by Solomon [63]. These functions can be defined in differentways. In this paper, following Lotka [64], we adopt f (u) = cu, (4) which is a linear functional response without saturation, where c > 0 ...

Are adults' and childrens' ascriptions of intention and allocations of punishment affected not only by the valence of a protagonist's intention (positive/negative), but also by the undesirability of (potentially unintended) outcome(s) of the protagonist’s action (e.g., something gets broken)? Even young children are sensitive to whether an outcome was intended when allocating blame/punishment (...

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington-DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient condit...

Many predators are able to become better at spotting cryptic prey by recognising specific clues, but by concentrating on one prey type they will become worse at spotting other prey types. This phenomenon is known as the formation of a search image for a certain prey by a predator and is related to apostatic selection. Here we study the evolution of a search image in the predator by formulating ...

An optimal control problem is studied for a predator-prey system with logistic growth rate of the prey and a prey-dependent functional response of the predator. The control function has two components and signifies the rate of mixture between the individuals of the species. The form of the optimal control is determined according to Pontryagin’s maximum principle. It is bang-bang and the number ...

In this paper, we systematically study the dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for the periodic (al...