[PDF] Top 20 Permanence, Almost Periodic Oscillations and Stability of Delayed Predator-Prey System with General Functional Response

... of predator- prey systems in mathematical ecology has a long history starting with the pioneering work of Lotka and Volterra [1- ...This general approach has been applied to many biological systems ... See full document

... dynamics system describes the current state of the population not only related to the current state but also related to the state of the population in the ...of stability, bifurcate into var- ious ... See full document

... a delayed ratio-dependent functional response predator-prey model with a threshold harvesting ...the system be- fore and after the ...and permanence properties are ... See full document

... the prey and ...the prey and predator popula- tion per unit area, ...For general nonautonomous case, Fan and Kuang studied the permanence, extinction, and global asymptotic ... See full document

... semi-ratio-dependent predator-prey system with Holling type IV functional response and time delay is ...the general nonautonomous system is permanent and globally ... See full document

... local stability of the posi- tive equilibrium and existence of the local Hopf bifurcation of system ...and stability of the bifurcated periodic solutions are de- termined by using the normal ... See full document

... years, predator-prey systems which model some biological phenomena and relationship between predators and preys in the real world play a crucial role in math- ...multiple periodic solutions for ... See full document

... a delayed continuous-time growth model with a special mound-shaped production ...a delayed-energy- based model of capital ...chain system with two delays by taking the sum of the two delays as the ... See full document

... In general, delay differential equations can exhibit much more complicated dynam- ics than differential equations without ...asymptotic stability of the positive equilibrium about stochastic ... See full document

... to prey x (respectively, to the predator ...global stability of positive equilibrium of system ...linearized stability and the global asymptotic stability of equilibria of ... See full document

... between predator and prey has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology due to its universal existence and ...the predator- prey ... See full document

... of system (3) in the interior of the first quadrant of R 2 ...the stability of fixed points of system (3) and rigorously prove that the map (3) undergoes the flip bifurcation and Hopf bifurcation by ... See full document

... Liapunov functional to ...of System F is K, ...that System F has an almost periodic solution pn such that β i ≤ p i n ≤ α i , i 1, 2, for all n ∈ ... See full document

... then for 0 < D < 1, we have 2 < γ(D) < δ(D) and both δ(D) and γ(D) are increasing with respect to D. See Figure 4.2. It is also known that (see Sugie [6]) system (4.2) has no limit cycles if either a ≤ ... See full document

... and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with ...its stability via the Hopf bifurcation when the time delay increases beyond a ... See full document

... “Almost periodic oscillation in a Watt-type predator- prey Model with diffusion and time delays,” IAENG International Journal of Applied Mathematics, ... See full document

... impulsive predator-prey dynamic systems on time scales calculus are ...the system has periodic solution is investigated, and three different conditions have been found, which are necessary for ... See full document

... the predator population will go into extinction, and the prey population will approach the carrying capacity ...susceptible prey are low, then the infected prey and predator population ... See full document

... stage-structured predator-prey model (stage structure on predators) with two discrete time delays has been ...the prey and their foods are provided by ...Linear stability analysis for both non ... See full document

... The rest of this paper is organized as follows: In Section 2, we present some basic materials on fractional calculus. A detailed analysis on the stability and Hopf bifurcation of the equilibria is carried out in ... See full document