Deformities in silver pomfret Pampus argenteus caught from Kuwait waters

During sampling for spawning stock of the silver pomfret,Pampus argenteus in Kuwait waters,a few seriously deformed individuals were captured.These individuals had been attacked and wounded,but had healed and survived.The fish body deformities are believed to be caused by predation attempts on silver pomfret by predators such as sharks,groupers,and croakers.

Optimal harvesting of a prey-predator model with variable carrying capacity

This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh-Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifur- cation occurs with respect to a parameter which is the ratio of predator＇s and prey＇s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin＇s maximum principle. Some numerical simulations are given to explain most of the analytical results.

HETEROCLINIC BIFURCATIONS OF A PREY-PREDATOR FISHERY MODEL WITH IMPULSIVE HARVESTING

In this paper, we consider a prey-predator fishery model with Allee effect and state- dependent impulsive harvesting. First, we investigate the existence of order-1 heteroclinic cycle. Second, choosing p as a control parameter, we obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system （2.3） by using the geometry theory of semi-continuous dynamic systems. Finally, on the basis of the theory of rotated vector fields, heteroclinic bifurcation to perturbed system of system （2.3） is also studied. The methods used in this paper are novel to prove the existence of order-1 heteroclinic cycle and heteroclinic bifurcations.

ROLE OF HARVESTING IN CONTROLLING CHAOTIC DYNAMICS IN THE PREDATOR-PREY MODEL WITH DISEASE IN THE PREDATOR

Predator prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

Prey-predator model with functional response for optimal harvesting incorporating prey refuge

This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey predator system parameter.

NONCONSTANT PREY HARVESTING IN RATIO-DEPENDENT PREDATOR-PREY SYSTEM INCORPORATING A CONSTANT PREY REFUGE

This paper deals with the problem of nonconstant harvesting of prey in a ratio-dependent predator-prey system incorporating a constant prey refuge. Here we use the reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagin＇s maximum principle. The key results developed in this paper are illustrated using numer- ical simulations. Our results indicate that dynamic behavior of the system very much depends on the prey refuge parameter and increasing amount of refuge could increase prey density and may lead to the extinction of predator population density.