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...

We propose a scaled version of the Rosenzweig-MacArthur model using both Type I and Type II functional responses that incorporates the size dependence of interaction rates. Our aim is to link the energetic needs of organisms with the dynamics of interacting populations, for which survival is a result of a game-theoretic struggle for existence. We solve the scaled model of predator-prey dynamics...

In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spati...

Ahmed [1], considered study of prey-predator model with predator in disease and harvesting. In this article, a ratio-dependent predator-prey model with disease in the prey population is formulated and analyzed. Assuming that prey populations suffered from epidemics and the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours ...

Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator d...

We model the effects of both stochastic and deterministic temperature variations on arthropod predator-prey systems. Specifically, we study the stochastic dynamics of arthropod predator-prey interactions under a vary ing temperature regime, and we develop an individual model of a prey under pressure from a predator, with vigilance (or foraging effort), search rates, at tack rates, and other pre...

   Scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. Thus, the harvested rate is used as the control parameters. Moreover, the study of harvested population dynamics is more realistic.    In the present paper, some predator-prey models in which two ecologically inte...

This is the first study analysing individual differences in shyness–boldness and behavioural asymmetries in young zebrafish larvae (fry, 7 days post-fertilisation). Individual differences were more stable in tests with predator model (crude image of a fish face) than with an arbitrary novel stimulus (vertical black stripe). Principal component analysis revealed a dimension of ‘shyness’ that inv...

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...