6,792 research outputs found
Periodic solutions of a delayed predator-prey model with stage structure for predator
A periodic time-dependent Lotka-Volterra-type predator-prey model
with stage structure for the predator and time delays due to
negative feedback and gestation is investigated. Sufficient
conditions are derived, respectively, for the existence and global
stability of positive periodic solutions to the proposed model
Global Property in a Delayed Periodic Predator-Prey Model with Stage-Structure in Prey and Density-Independence in Predator
We study the global property in a delayed periodic predator-prey model with stage-structure in prey and density-independence in predator. The sufficient conditions on the ultimate boundedness of all positive solutions are obtained, and the sufficient conditions of the integrable form for the permanence and extinction are further established, respectively. Some well-known results on the predator density-dependency are improved and extended to the predator density-independent cases. The theoretical results are confirmed by the special examples and the numerical simulations
Theoretical Study of Pest Control Using Stage Structured Natural Enemies with Maturation Delay: A Crop-Pest-Natural Enemy Model
In the natural world, there are many insect species whose individual members
have a life history that takes them through two stages, immature and mature.
Moreover, the rates of survival, development, and reproduction almost always
depend on age, size, or development stage. Keeping this in mind, in this paper,
a three species crop-pest-natural enemy food chain model with two stages for
natural enemies is investigated. Using characteristic equations, a set of
sufficient conditions for local asymptotic stability of all the feasible
equilibria is obtained. Moreover, using approach as in (Beretta and Kuang,
2002), the possibility of the existence of a Hopf bifurcation for the interior
equilibrium with respect to maturation delay is explored, which shows that the
maturation delay plays an important role in the dynamical behavior of three
species system. Also obtain some threshold values of maturation delay for the
stability-switching of the particular system. In succession, using the normal
form theory and center manifold argument, we derive the explicit formulas which
determine the stability and direction of bifurcating periodic solutions.
Finally, a numerical simulation for supporting the theoretical analysis is
given.Comment: 28 pages, 9 figure
Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay
We propose a prey predator model with stage structure for prey. A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered. Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated. By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively. It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value. According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem. Numerical simulations are carried out to show consistency with theoretical analysis
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