Accurate parametrization of functional terms in model equations is of great importance for reproducing the dynamics of real food webs. Constructing models over large spatial and temporal scales using mathematical expressions obtained based on microcosm experiments can be erroneous. Here, using a generic spatial predator-prey model, we show that scaling up the microscale functional response of a...

In this paper, effect of alternative resource for top predator in food chain model with holling type III functional response is seen . Proposed model is demonstrated in respect of analytical as well numerical results. Bifurcation study with the variation of alternative resource and half saturation constants are done numerically. Simulation results shows that suitable alternati...

In biomathematics, many mathematical models have been established to describe the relationships between species and the outer environment, and the connections between different species. Among the relationships between the species living in the same outer environment, the predator-prey theory plays an important and fundamental role. The dynamic relationship between predators and their prey has l...

It is known that one of important factors impacted on a predator-prey system is the functional response. Holling proposed three types of functional response functions, namely, Holling I, Holling II, and Holling III, which are all monotonously nondescending 1 . But for some predator-prey systems, when the prey density reaches a high level, the growth of predator may be inhibited; that is, to say...

By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least two positive almost periodic solutions of harvesting predator-prey model with Holling III type functional response and time delays. An example and numerical simulations are employed to illustrate the main result of this paper. Key–Words: Almost periodicit...

Food-web population models are rather sensitive to parameterization of functional response in predation terms. Theoretical studies predict enhancing of ecosystems' stability for a functional response of sigmoid type (Holling type III). The choice of a correct type of response is especially important for modelling outcome of grazing control of algal blooms by zooplankton in nutrient-rich ecosyst...

Recently, there were many works on predator-prey system done by scholars [1–6]. In particular, since Hassell-Varley [7] proposed a general predator-prey model with Hassell-Varley type functional response in 1969, many excellent works have been conducted for the Hassell-Varley type system [1, 7–13]. Liu and Huang [8] studied the following discrete predator-prey system with Hassell-Varley-Holling...

In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some ...

Abstract In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory by constructing suitable functional, obtain some sufficient conditions for existence uniqueness of positive solutions asymptotic equilibrium to system. Finally, give numerical examples illustrate feasibility our resu...