Although predators affect prey both via consumption and by changing prey migration behavior, the interplay between these two effects is rarely incorporated into spatial models of predator-prey dynamics and competition among prey. We develop a model where generalist predators have consumptive effects (i.e., altering the likelihood of local prey extinction) as well as nonconsumptive effects (alte...

fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

‎in this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (pmsm) system. the necessary condition for the existence of chaos in the fractional-order pmsm system is deduced and an active controller is developed based on the stability theory for fractional systems. the presented control scheme  is simple and flexible, and it is suitable both fo...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

Predators use cues associated with their prey to assess prey quality and to avoid consuming poisonous prey. Considerable attention has been given to predators' use of aposematic cues to assess prey quality, but little is known about predators that eavesdrop on prey cues that are not intended for them. Here we investigate the prey-cue/prey-quality associations of a predator that eavesdrops on th...

Resource availability and accessibility are primary factors guiding the distribution and abundance of organisms. For generalists, prey availability reflects both prey abundance and differences in quality among prey taxa. Although some aspects of prey quality, such as nutritional composition, are well studied, our understanding of how prey morphology contributes to overall prey quality is limite...

Hundreds of studies exist on predator foraging behaviour, and the same holds for anti-predator behaviour in prey. However, despite these many studies, almost nothing is known about diet choice by predators that feed on prey with anti-predator behaviour. We addressed this problem theoretically by incorporating anti-predator vigilance into two classical models of diet choice by predators. Vigilan...

1. Current formulations of functional responses assume that the prey is homogeneous and independent of intraspecific processes. Most prey populations consist of different coexisting size classes that often engage in asymmetrical intraspecific interactions, including cannibalism, which can lead to nonlinear interaction effects. This may be important as the size structure with the prey could alte...