Crowley Martin Type Functional Response Research Articles

Impact of generalist type sexually reproductive top predator interference on the dynamics of a food chain model

Food uptake ability of higher trophic level species are more complicated and interesting due to their choice and availability of food and consequently their growth. In the present study, the effect of top predator interference on the dynamics of a tritrophic food chain model involving an intermediate and a generalist type top predator are considered. It is assumed that the interaction between the logistically growing prey and intermediate predator follows the Volterra scheme, while that between the top predator and its favorite food i.e. the intermediate predator follows Crowley–Martin type functional response. Also, it is considered that the growth of top predator is by sexual reproduction. The boundedness of the system, existence of an attracting set, local and global stability of non-negative equilibrium points and uniform persistence are established by very complicated and highly nonlinear biological considerations. With the help of empirical results from different field and laboratory experiment, it is clarified that Crowley–Martin type functional response gives better result than other predator dependent functional responses for the issue of interference among own population. Also it is clarified from literature survey that high trophic species are mostly generalist type i.e. they can survive rather than their favorite food depending upon the present environmental situation and their growth rate depends upon the mating success. Moreover, increasing the top predator interference stabilizes the system, while increasing the normalization of the residual reduction in the top predator population destabilizes the system. Different numerical examples support these ecological phenomenon.

Spatial, temporal and spatiotemporal patterns of diffusive predator–prey models with mutual interference

In this paper, the spatial, temporal and spatiotemporal dynamics of a reaction–diffusion predator–prey system with mutual interference described by the Crowley–Martin-type functional response, under homogeneous Neumann boundary conditions, are studied. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equations is presented. For the reaction–diffusion model, firstly the invariance, uniform persistence and global asymptotic stability of the coexistence equilibrium are discussed. Then it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Next it is proved that the model exhibits Hopf bifurcation which produces temporal inhomogeneous patterns. Furthermore, at the points where the Turing instability curve and Hopf bifurcation curve intersect, it is demonstrated that the model undergoes Turing–Hopf bifurcation and exhibits spatiotemporal patterns. Finally, the existence and non-existence of positive non-constant steady states of the reaction–diffusion model are established. Numerical simulations are presented to verify and illustrate the theoretical results.

Competition between Two Microorganisms in a Crowley-Martin Type Chemostat with Pulsed Input and Washout

In this paper, we introduce and study a competition Chemostat model with Crowley-Martin type functional response and pulsed input and washout. The stability of the boundary periodic solutions is investigated. We get that above some threshold there are periodic oscillations in substrate and microorganisms, which implies the coexistence of two species.

The asymptotic behavior of a Chemostat model with Crowley–Martin type functional response and time delays

In this paper, we introduce an improved Chemostat model with Crowley–Martin type functional response and time delays. By constructing Lyapunov functionals, the global asymptotic stability of the equilibria is shown in the case of a single species. The conditions for the global asymptotical stability of the model with time delays are obtained via monotone dynamical systems in the case of two species. Our results demonstrate that the effects of predator interference may result in coexistence of two species.

Analysis for a Food Chain Model with Crowley–Martin Functional Response and Time Delay

This paper is concerned with a nonautonomous three species food chain model with Crowley–Martin type functional response and time delay. Using the Mawhin’s continuation theorem in theory of degree, sufficient conditions for existence of periodic solutions are obtained. Keywords—Periodic solutions; coincidence degree; food chain model; Crowley–Martin functional response.

Dynamics of a three species food chain model with Crowley–Martin type functional response

In this paper, a three species food chain model, consisting of a hybrid type of prey-dependent and predator-dependent functional responses, is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence conditions are established. Bifurcation diagrams are obtained for biologically feasible parameters. The results show that the system exhibits rich complexity features such as stable, periodic and chaotic dynamics.