Abstract
This paper presents a singular prey-predator fishery model, where maturation delay for prey and gestation delay for predator are considered. Fishing efforts are introduced to harvest prey and predator population, which are developed as control instruments to investigate optimal utilization of fishery resource. By analyzing associated characteristic equation, local stability analysis is studied due to combined variations of double time delays. Furthermore, Pontryagin’s maximum principle is utilized to characterize optimal harvest control, and the optimality system is numerically solved based on an iterative method.
Highlights
According to statistics from the Food and Agriculture Organization of United Nations [1], approximate fifty-three percent of fish stock under observation has experienced overexploitation or depletion, which reiterate the fact that fishery needs to be managed with an effective and carefully defined objective to prevent overexploitation and replenish depleted stock [1]
By incorporating maturation delay for prey population and gestation delay for predator population, we extend work done in [5]
Fishing efforts are introduced to commercially harvest prey population and predator population, which are developed as control instruments to investigate optimal utilization of prey-predator fishery resource
Summary
According to statistics from the Food and Agriculture Organization of United Nations [1], approximate fifty-three percent of fish stock under observation has experienced overexploitation or depletion, which reiterate the fact that fishery needs to be managed with an effective and carefully defined objective to prevent overexploitation and replenish depleted stock [1]. In [5], authors establish a dynamic model where both prey and predator fishery resource population are exploitable, which is as follows: ẋ (t). Many theoreticians and experimentalists have investigated complex dynamics of prey-predator fishery system [16, 17]; it reveals that time delay may cause the loss of stability and other complicated dynamical behavior such as the periodic structure and bifurcation phenomenon [15, 18, 19]. Keeping these aspects in view, we will extend work in [5] by incorporating maturation delay for prey and gestation delay for predator into system (1).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
