2,995 research outputs found
Stochastic Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-IV Functional Response
We consider an additional food provided prey-predator model exhibiting
Holling type IV functional response with combined continuous white noise and
discontinuous L\'evy noise. We prove the existence and uniqueness of global
positive solutions for the considered model. By considering the quality and
quantity of additional food as control parameters, we formulate a time-optimal
control problem. We obtain the condition for the existence of an optimal
control. Furthermore, making use of the arrow condition of the sufficient
stochastic maximum principle, we characterize the optimal quality of additional
food and optimal quantity of additional food. Numerical results are given to
illustrate the theoretical findings with applications in biological
conservation and pest management
Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-III and Holling Type-IV Functional Responses
In recent years, time-optimal control studies on additional food provided
prey-predator systems have gained significant attention from researchers in the
field of mathematical biology. In this study, we initially consider an
additional food provided prey-predator model exhibiting Holling type-III
functional response and the intra-specific competition among predators. We
prove the existence and uniqueness of global positive solutions for the
proposed model. We do the time optimal control studies with respect quality and
quantity of additional food as control variables by transforming the
independent variable in the control system. Making use of the Pontraygin
maximum principle, we characterize the optimal quality of additional food and
optimal quantity of additional food. We show that the findings of these
time-optimal control studies on additional food provided prey-predator systems
involving Holling type III functional response have the potential to be applied
to a variety of problems in pest management. In the later half of this study,
we consider an additional food provided prey-predator model exhibiting Holling
type-IV functional response and study the above aspects for this system
Recommended from our members
Global dynamics of a state-dependent feedback control system
The main purpose is to develop novel analytical techniques and provide a comprehensive qualitative analysis of global dynamics for a state-dependent feedback control system arising from biological applications including integrated pest management. The model considered consists of a planar system of differential equations with state-dependent impulsive control. We characterize the impulsive and phase sets, using the phase portraits of the planar system and the Lambert W function to define the Poincaré map for impulsive point series defined in the phase set. The existence, local and global stability of an order-1 limit cycle and sharp sufficient conditions for the global stability of the boundary order-1 limit cycle have been provided. We further examine the flip bifurcation related to the existence of an order-2 limit cycle. We show that the existence of an order-2 limit cycle implies the existence of an order-1 limit cycle. We derive sufficient conditions under which any trajectory initiating from a phase set will be free from impulsive effects after finite state-dependent feedback control actions, and we also prove that order-k (k ≥ 3) limit cycles do not exist, providing a solution to an open problem in the integrated pest management community. We then investigate multiple attractors and their basins of attraction, as well as the interior structure of a horseshoe-like attractor. We also discuss implications of the global dynamics for integrated pest management strategy. The analytical techniques and qualitative methods developed in the present paper could be widely used in many fields concerning state-dependent feedback control
- …