Complex dynamics of a discrete-time prey-predator system with Allee effect

In this paper, we investigate the stability and bifurcation of a discrete-time prey-predator system which is subject to an Allee effect on prey population. It is concluded that the system undergoes flip and Neimark- Sacker bifurcations in a small neigborhood of the unique positive fixed point which depends on the number of prey-predator. The chaotic behavior that emerges with Neimark-Sacker bifurcation is controlled by the OGY method and hybrid control method. Moreover, the numerical simulations are done to demonsrate the theoratical results.

The Microbiota of a Mite Prey-predator System on Different Host Plants Are Characterized by Functional Redundancy and Dysbiosis

Microbiota have diverse roles in the life cycles of their hosts, affecting their growth, development, behavior, and reproduction. Changes in physiological conditions of the host can also impact the assemblage of host-associated microorganisms. However, little is known of the effects of host plant–prey–predatory mite interactions on mite microbiota. We compared the microbial communities of eggs and adult females of the two˗spotted spider mite Tetranychus urticae Koch (Acari: Tetranychidae) and of adult females of the predatory mite Neoseiulus californicus (McGregor) (Acari: Phytoseiidae) on four different host plants (cotton, maize, pinto bean, and tomato) by metabarcoding sequencing of the V3–V4 region of the 16S ribosomal RNA gene (16S rRNA), using the Illumina MiSeq platform. Only the egg microbiota of T. urticae was affected by the host plant. The microbiota of the predatory mite N. californicus was very different from that of its prey, and the predator microbiota was unaffected by the different host plant–prey systems tested. Only the microbiota of the eggs of T. urticae carried Serratia as a high fidelity-biomarker. Biomarker bacteria were also detected in the microbiota of adult females of T. urticae and N. californicus, with different biomarkers in each host-plant species. The microbiota associated with eggs and adult females of T. urticae and adult females of N. californicus differed in their potential contributions to the host mite.

The Connection Matrix analysis of a Prey-Predator system with a Strong Allee effect and multiple interior equilibria

We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.

An Eco-Epidemiological Model Incorporating Harvesting Factors

The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations.

Influence of the Fear Effect on a Holling Type II Prey–Predator System with a Michaelis–Menten Type Harvesting

In this work, a prey–predator system with Holling type II response function including a Michaelis–Menten type capture and fear effect is put forward to be studied. Firstly, the existence and stability of equilibria of the system are discussed. Then, by considering the harvesting coefficient as bifurcation parameter, the occurrence of Hopf bifurcation at the positive equilibrium point and the existence of limit cycle emerging through Hopf bifurcation are proved. Furthermore, through the analysis of fear effect and capture item, we find that: (i) the fear effect can either stabilize the system by excluding periodic solutions or destroy the stability of the system and produce periodic oscillation behavior; (ii) increasing the level of fear can reduce the final number of predators, but not lead to extinction; (iii) the harvesting coefficient also has significant influence on the persistence of the predator. Finally, numerical simulations are presented to illustrate the results.

Stability and bifurcations of a discrete-time prey-predator system with constant prey refuge

In ecology, by refuge an organism attains protection from predation by hiding in an area where it is unreachable or cannot simply be found. In population dynamics, once refuges are available, both prey-predator populations are expressively greater and meaningfully extra species can be sustained in the region. This examine the stability of a discrete predator prey model incorporating with constant prey refuge. Existence results and the stability conditions of the system are analyzed by obtaining fixed points and Jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Numerical experiments are simulated for the better understanding of the qualitative behavior of the considered model. Mathematics Subject Classification. [2010] : 37C25, 39A28, 39A30, 92D25.