The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density...

This paper concerns with a new delayed predator–prey model with stage structure on prey, in which the immature prey and the mature prey are preyed by predator and the delay is the length of the immature stage. Mathematical analysis of the model equations is given with regard to invariance of non-negativity, boundedness of solutions, permanence and global stability and nature of equilibria. Our ...

Seasonal changes in the diel feeding patterns of the zooplanktivorous icefish (Neosalanx taihuensis), which is an endemic species of China, were studied in the large, shallow eutrophic Lake Chaohu of China during the autumn of 2002 and summer of 2003. The results of the diel feeding rhythm indicate that icefish is a visual particulate feeder. There were large differences in diet composition and...

In this talk we discuss the predator-prey models with harvesting of the prey. We briefly introduce the basic Lotka-Volterra predator-prey model and different harvesting strategies. Then we focus on two types of harvesting functions, and combine them with two types of predator-prey models, one with exponential growth of the prey and the other one with logistic growth of the prey. For each type o...

Developmental studies have shown that environmental stimulation received by a developing sensory system can alter the developmental outcome of both that sensory system and other aspects of the nervous system. We investigated the ecologically relevant question of whether prior exposure to prey early in development within one sensory modality could influence later prey choice within a different s...

We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the susceptible prey survive, or the disease becomes endemic, but the predators are wiped out. Another alternative is that the disease is eradicated, with sound prey a...

Predator-prey models consider those prey that are free. They assume that once a prey is captured by a predator it leaves the system. A question arises whether in predator-prey population models the variable describing prey population shall consider only those prey which are free, or both free and handled prey together. In the latter case prey leave the system after they have been handled. The c...

The functional response of the tiger beetle Megacephala carolina carolina L. (Coleoptera: Carabidae) was determined on adult twolined spittlebug, Prosapia bicincta (Say) (Hemiptera: Cercopidae), and fourth instars of fall armyworm, Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae), in single-prey and two-prey systems. In the laboratory,M. carolina carolina demonstrateda type II functi...

One may find out the application‎ ‎of mathematics in the areas of ecology‎, ‎biology‎, ‎environmental‎ ‎sciences etc‎. ‎Mathematics is particulary used in the problem of‎ ‎predator-prey known as lotka-Volterra predator-prey equations.‎ ‎Indeed‎, ‎differential equations is employed very much in many areas‎ ‎of other sciences‎. ‎However‎, ‎most of natural problems involve some‎ ‎unknown functions...

In the current paper, we propose a two-prey-one-predator system with Holling type II predation functional response where prey species consumes the remains of the other prey species’ carcass given by their predator. Mathematical analysis of the proposed model equations with regard to non-negative invariance including stability and bifurcation are carried out. Next, we extend the deterministic sy...