Further investigations into the stability and bifurcation of a discrete predator–prey model

Complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response

“…( In order to investigate the local stability and bifurcation for an equilibrium point of a general 2D system, the following lemma will be very useful and even essential; for the details see [24].…”

“…For instance, the single-species discrete-time models have bifurcations, chaos and more complex dynamical behaviors (see [6,[12][13][14][15][16][18][19][20][21][22]). For the flip bifurcation and Hopf bifurcation of discrete models, see also [6,[12][13][14]24].…”

Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response

“…Zhang et al [26] investigated the dynamical behaviors of the discrete-time predator-prey biological economic system by using new normal form of differential-algebraic system. Wang and Li [24] revisited a discrete predator-prey model and proposed a very meaningful lemma which can be used to study the system's stability and bifurcation. Elabbasy et al [5] derived the existence and stability of the fixed points of a discrete reduced Lorenz system by using the center manifold theorem and bifurcation theory.…”

Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission

“…Zhao et al [23] focused on a reaction-diffusion neural network with delays and studied the stability and bifurcation of the networks. Wang and Li [20] revisited a discrete predator-prey model with a non-monotonic functional response and presented a very useful lemma which is a corrected version of a known result, and a key tool to study the local stability and bifurcation of the system.…”

“…Hu et al [15] investigated the flip bifurcation and Hopf bifurcation of a discrete-time SIR epidemic model by using the center manifold theorem and bifurcation theory. Wang et al [20] formulated an easily verified and complete discrimination criterion for the local stability of the two equilibria of a discrete predator-prey model with a non-monotonic functional response, and then studied the stability and bifurcation for the equilibrium point. Hu et al [12] discussed the globally stability of a SIR epidemic model with the saturated contact rate and vertical transmission by using V function and Dulac function.…”