Stability analysis of a delayed predator–prey model with nonlinear harvesting efforts using imprecise biological parameters

In this paper, the dynamical behaviors of a delayed predator–prey model (PPM) with nonlinear harvesting efforts by using imprecise biological parameters are studied. A method is proposed to handle these imprecise parameters by using a parametric form of interval numbers. The proposed PPM is presented with Crowley–Martin type of predation and Michaelis–Menten type prey harvesting. The existence of various equilibrium points and the stability of the system at these equilibrium points are investigated. Analytical study reveals that the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate the main analytical findings.

Bifurcation analysis in a diffusive phytoplankton–zooplankton model with harvesting

A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the harvesting as the parameter, we get the existence and stability of the positive steady state, and also investigate the existence of spatially homogeneous and inhomogeneous periodic solutions. Then, by applying the normal form theory and center manifold theorem, we give the stability and direction of Hopf bifurcation from the positive steady state. In addition, we also prove the existence of the Bogdanov–Takens bifurcation. These results reveal that the harvesting and diffusion really affect the spatiotemporal complexity of the system. Finally, numerical simulations are also given to support our theoretical analysis.

Complex Dynamical Behavior of a Three Species Prey–Predator System with Nonlinear Harvesting

In this manuscript, we consider an extended version of the prey–predator system with nonlinear harvesting [Gupta et al., 2015] by introducing a top predator (omnivore) which feeds on more than one trophic levels. Consideration of third species as omnivore makes the system a food web of three populations. We have guaranteed positivity as well as the boundedness of solutions of the proposed system. We observed that the presence of third species complicates the dynamical behavior of the system. It is also observed that multiple positive steady states exist for the proposed system which makes the problem more interesting compared to the similar models studied previously. Sotomayor’s theorem is being utilized to study the saddle-node bifurcation. The persistence conditions are discussed for the proposed model. The local existence of periodic solution through Hopf bifurcations is also guaranteed numerically. It is observed that the proposed model is capable to exhibit more complicated dynamics in the form of chaos in both the cases when there are unique and multiple coexisting steady states. Bifurcation diagrams and Lyapunov exponents have been drawn to ensure the existence of chaotic dynamics of the system.

Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting

A single species stage structure model with Michaelis–Menten-type juvenile population harvesting is proposed and investigated. The existence and local stability of the model equilibria are studied. It shows that for the model, two cases of bistability may exist. Some conditions for the global asymptotic stability of the boundary equilibrium are derived by constructing some suitable Lyapunov functions. After that, based on the Bendixson–Dulac discriminant, we obtain the sufficient conditions for the global asymptotic stability of the internal equilibrium. Our study shows that nonlinear harvesting can make the dynamics of the system more complex than linear harvesting; for example, the system may admit the bistable stability property. Numeric simulations support our theoretical results.

The Dynamics of an Eco-Epidemiological Model with Allee Effect and Harvesting in the Predator

The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of the system.