Hopf bifurcation of a predator–prey system with predator harvesting and two delays

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

“…Hence, system (7) not only investigates interaction and coexistence mechanism of population, but also studies the dynamical behavior due to variation of economic interest of commercial harvesting. The algebraic equations proposed in previous related differential algebraic bioeconomic systems [33,34,[38][39][40]42,43,45,46] also concentrate on the economic interest of commercial harvesting. However, the price of harvested population and cost of commercial harvesting are all constants, which is unrealistic in the real world.…”

“…Furthermore, time delays for prey and predator population of systems proposed in [33,34,[38][39][40]42,43,46,47] are assumed to be the same discrete value, and system with two delays in [45] is investigated by using the equivalent system with a single time delay. The biological characteristics differences between prey and predator population are not considered in the above mentioned work, which contradicts to the realistic situation in the real world.…”

“…(5) Recently, some delayed differential-algebraic systems are constructed to discuss dynamic effect of economic interest of commercial harvesting on prey-predator system [33,34,38,39,42,43,45,46]. They are established by several delayed differential equations and an algebraic equation.…”

“…(5). Compared with the harvested models proposed in previous related work (see [26,28,37] and the references therein), advantages of systems proposed in [33,34,38,39,42,43,45,46] are that these models not only investigate interaction mechanism of population, but also offer a simpler way to explore dynamical behavior due to variation of economic interest of commercial harvesting. However, time delays for prey and predator population of systems proposed in [33,34,38,39,42,43,46] are assumed to be the same discrete value, and system with two delays in [45] is investigated by using the equivalent system with a single time delay.…”

“…However, price of harvested population and cost of commercial harvesting are all constants, which are unrealistic in the real world. As introduced in system (7), price and cost considered in system (7) are expressed by time-varying function associated with fluctuation of harvested predator population density, which extend form of algebraic equations proposed in [33,34,38,39,42,43,45,46] in a more realistic way.…”