[PDF] Top 20 Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting

... sidered predator–prey models with harvesting. The harvesting can be mainly divided into three types: (i) constant harvesting, (ii) proportional harvesting, and (iii) ... See full document

... and harvesting in prey population, and found that optimal harvesting policy is dependent on both gestation delay and Allee ...a harvesting predator-prey model with ... See full document

... on Hopf bifurcation analysis including the existence of Hopf bifurcation, bifurcation direction, and the stability of the bifurcating periodic solution by the theory of normal form and ... See full document

... discussed predator–prey models with these fac- ...a predator–prey system with time delay and studied the effect of time delay on the ...time delay. They found that a ... See full document

... the prey-nullclines and the red lines are the ...of predator-nullcline for four different values of ...(the prey nullcline is below the predator nullcline), suggesting there is no equilibrium ... See full document

... diffusive predator–prey model with lo- gistic prey growth rate [6–10] or strong Allee effect in prey ...This model, also known as the Holling–Tanner model, has been studied ... See full document

... of predator-prey systems that use a typical Lotka-Volterra inter- action ...the model, we should add a time delay to the model, and system ... See full document

... harvested predator species on a Holling type IV Prey-Predator model involving intra-specific ...competition. Prey-predator model has received much attention during the ... See full document

... to the gestation of the predator into system (.). Sufficient conditions were obtained for the global stability of the boundary equilibrium and the global attractivity of the positive equilibrium of the ... See full document

... of harvesting of competition species, specially the effect of constant rate harvesting on the prey-predator systems ...stability, Hopf bifurcation, limit cycles of the ...the ... See full document

... time delay are much more realistic, as in reality time delays occur in almost every biological problem and assumed to be one of the reasons of regular fluctuations in population density ...time delay. Also ... See full document

... Agarwal, M. and Pathak, R. (2012). Harvesting and Hopf Bifurcation in a prey- predator model with Holling Type IV Functional Response. International Journal of Mathematics and ... See full document

... the Hopf bifurcation for the predator-prey system have been discussed by using normal form theory and center manifold theory ...network model with two delays have been investigated ... See full document

... This paper is organized as follows. In Section 2, we investigate the existence and stability of equilibria. Dynamical behavior in the small neighborhood of the equilibria is also discussed. We show that all solutions of ... See full document

... the predator-prey-mutualist models have been studied by several scholars ...mutualistic model with saturating terms and effects of toxic substances, investigate the permanence of the system, and study ... See full document

... of Hopf bifurcation and stability of the bifurcating periodic solution of the controlled system are ...supercritical Hopf bifurcation and stable bifurca- tion periodic solutions are in ... See full document

... response predator-prey model with a threshold harvesting ...threshold harvesting can improve the undesirable behavior such as nonexistence of interior ...the model as well as ... See full document

... of predator-prey systems is one of the dominant subjects in ecology and mathematical ecology since Lotka [1] and Volterra [2] proposed the well- known predator-prey model ...of ... See full document

... fractional-order prey–predator systems, such as stability, bifurcations, chaos, have been researched by many investigators ...of predator-extinction equilibrium point and coexistence equilibrium ... See full document

... first predator-prey model on the basis of population ...ical model. For example, the authors in [3] analyzed the multiple bifurcation problem of a predator-prey ... See full document