[PDF] Top 20 Stability and bifurcation analysis of a discrete predator–prey system with modified Holling–Tanner functional response

... Predator–prey interactions have long been studied and continue to be one of the dominant themes in both biology and mathematical biology due to their universal existence and im- portance [1]. Recently, a ... See full document

... harvested predator-prey system with Holling type III functional response is ...global stability properties of the equilibria and the existence and uniqueness of limit ... See full document

... the bifurcation diagrams, phase portraits and Lyapunov exponents of system () to confirm the previous analytic results and show some new interesting complex dynamical behaviors existing in system ... See full document

... global stability of the positive equilibrium of ...of prey by the predator throughout its past history governs the present birth rate of the ...ratio-dependent Holling-Tanner ... See full document

... a system when two species interact with each other in the same ...by discrete times models. Discrete time models are easy to formulate and to simulate ...ratio-dependent discrete ... See full document

... and Holling type-IV functional ...model system using qualitative analysis, bifurcation theory and singular optimal ...the system under goes a Hopf bifurcation with respect ... See full document

... the stability of the system via bifurcations and even lead the system to ...the stability of the system and control the amplitude of the bifurcated periodic solution ...delayed ... See full document

... ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting in presence of white noise terms to understand the dynamics in presence of ... See full document

... of prey and predators; A, a, b, d, n, m, h, δ are positive constants; τ demonstrates the time delay because of the gestation of the predator; m and h measure the effects of capture rate and handling time, ... See full document

... a discrete-time prey-predator system with Holling type-IV function response in the presence of some alternative food to predator and harvesting of prey ... See full document

... a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response, which is the discrete version of the continuous ... See full document

... detailed analysis on the stability and Hopf bifurcation of the equilibria is carried out in Section ...the system by computing different orbits of the fractional ... See full document

... The predator–prey model is a very important population dynamics ...the functional response, based on ratio, age, or gender struc- ture, reaction–diffusion, ...the stability of the ... See full document

... The predator–prey models have a theoretical and practical ...of predator–prey ...the prey consump- tion rate by a predator is directly proportional to the prey ...that ... See full document

... a discrete semi-ratio- dependent prey-predator ...delayed discrete prey-predator system with the help of Lyapunov ...a discrete prey-predator ... See full document

... a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos ...and ... See full document

... existence, stability, and instability of the equilibria of the model and the boundedness of the solutions of the sys- tem ...global stability of the unique positive equilibrium are ...Hopf ... See full document

... the prey environment carrying ...the prey provides for conversion into predator ...of prey necessary to achieve one-half of the maximum rate ... See full document

... as Holling type functional response, where h is the handling time of predators, λ is the attack efficiency of predator to prey population, the exponent n describes the shape of the ... See full document

... Among other things, we are interested in positive solutions of (1.2). We call (u, v) a positive solution when u > 0 and v > 0 satisfies (1.2). Hence a positive solution is corresponding to a coexistence steady state ... See full document