[PDF] Top 20 Permanence of a Gilpin Ayala predator prey system with time dependent delay

... Predator-prey phenomena are always interesting topics in both ecology and mathematical ecology, which attract a lot of attention due to its universal existence and importance []. Since Volterra [] ... See full document

... stochastic Gilpin-Ayala predator-prey system with time-varying delays, and obtained the long-term gradual progress, mean estimation and population extinction of the ...stochastic ... See full document

... classical predator-prey system has gained an important theo- retical and practical significance, which has been studied extensively, and many excellent results concerning the permanence, ... See full document

... For the general nonautonomous case, they addressed properties such as permanence, extinction, and globally asymptotic stability of the system. For the periodic almost periodic case, they established ... See full document

... semi-ratio- dependent prey-predator ...discrete prey-predator system with the help of Lyapunov ...discrete prey-predator system and obtained conditions for ... See full document

... the predator death rate and half capturing saturation constant, ...respectively. System (.) was system- atically studied by Kuang and Beretta [], and the global stability of boundary equilibria, ... See full document

... know that the prey population and predator population obey the logistic growth. But many authors have suspected the reasonableness of the logistic equations [16,17]. Hence, some of them proposed single ... See full document

... The system is subject to no-flux boundary conditions, and it means that the ecology system is ...corresponding delay system without diffusion and ratio-dependent functional response and ... See full document

... response predator-prey model with a threshold harvesting ...the system be- fore and after the ...and permanence properties are examined too. Then we analyze the effect of time ... See full document

... on time scales was initiated by Hilger [] in order to unify continu- ous and discrete analysis, and it has become an effective approach to the study of mathe- matical models involving the hybrid ... See full document

... the Gilpin–Ayala models are more advanta- geous because the rate of change in the size of each species is a nonlinear function of the sizes of the interacting species in the Gilpin–Ayala ... See full document

... medical system, when we take chemotherapeutic drugs for can- cer patients,cancer cells will decrease rapidly, but at the same time, drugs do harm to normal cells and body’s immune function; see [17] and the ... See full document

... Abstract —A stochastic predator-prey system in- volving time-varying delays is considered. Some new sufficient conditions for existence, extinction and global asymptotical stability are ... See full document

... discrete-time predator-prey ...the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation by using center manifold theorem and bifurcation ... See full document

... the predator-prey systems without ...some predator-prey sys- tems under constant rate ...delayed predator-prey patch systems with periodic ... See full document

... the system parameters such that trajectories starting from the domain of interest can reach the zero equilibrium following any fixed ...ratio- dependent predator-prey model where ... See full document

... stage-structured predator-prey model incor- porating time delay with prey growth subject to a strong Allee ...of system (3), and find birth rate plays an important role in the ... See full document

... two-species predator-prey system of population allelopathy with discrete delay is ...the system at the positive equilibrium and analyzing the associated characteristic equation, the ... See full document

... Leslie-Gower predator- prey model with Holling-type II schemes and a prey ...the permanence of the system, after that, by constructing a suitable Lyapunov function, we also investigate ... See full document

... of time-delay induced Hopf bifurcation in a delayed predator-prey system with ...of time delay, but loses its stability via the Hopf bifurcation when the time ... See full document