On a predator prey model with nonlinear harvesting and distributed delay

A predator prey model with nonlinear harvesting (Holling type-II) with both constant and distributed delay is considered. The boundeness of solutions is proved and some sufficient conditions ensuring the persistence of the two populations are established. Also, a detailed study of the bifurcation of positive equilibria is provided. All the results are illustrated by some numerical simulations.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía

Stability and Bifurcation Analysis of a Delayed Three Species Food Chain Model with Crowley-Martin Response Function

In this paper we have studied the dynamical behaviors of three species prey-predator system. The interaction between prey and middle-predator is Crowley-Martin type functional response. Positivity and boundedness of the system are discussed. Stability analysis of the equilibrium points is presented. Permanence and Hopf-bifurcation of the system are analyzed under some conditions. The effect of discrete time-delay is studied, where the delay may be regarded as the gestation period of the super-predator. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Extensive numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically

Bifurcation analysis for a delayed food chain system with two functional responses

A delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, using the normal form theory and center manifold theorem, the properties of Hopf bifurcation such as direction and stability are determined. Finally, numerical simulations are given to substantiate the theoretical results

Dynamics of a diffusive predator-prey system with fear effect in advective environments

We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary conditions, as well as Free-Flow (FF) boundary conditions. Our investigation focuses on determining the direction and stability of spatial Hopf bifurcation, with the generation delay $\tau$ serving as the bifurcation parameter. Additionally, we examine the influence of both linear and Holling-II functional responses on the dynamics of the model. Through these analyses, we aim to gain a better understanding of the intricate relationship between advection, predation, and prey response in this system