2018 **Abstract:** In this paper, we consider the complex dynamics of 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 system in (Nonlinear Anal., Real World Appl. 16:235-249, 2014). First, by giving several examples to display the limitations and errors of the local stability of the equilibrium point p obtained in (Nonlinear Anal., Real World Appl. 16:235-249, 2014), we provide an easily verified and complete discr…

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“…In order for the map (14) to undergo a period-doubling bifurcation, we require that the following discriminatory quantities are non-zero:…”

confidence: 99%

“…In order for the map (14) to undergo a period-doubling bifurcation, we require that the following discriminatory quantities are non-zero:…”

confidence: 99%

“…For example, a discrete-time model with a single species can display chaos and more complex dynamical behavior, but chaos requires at least three species in a continuous-time model (see literature [3][4][5][6][7][8] ). Discrete-time and continuous-time models that regulate population systems can be found in previous studies [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references listed therein. Many of these studies have used the logistic map to represent the growth in the prey population.…”

confidence: 99%

“…Moreover, the interplay between the species may lead to dynamics of stunning complexity. There is a vast literature regarding such models and models which also include age or stage structure, see [15][16][17][18][19][20][21][22][23][24][25], and more recently, cf [26][27][28][29] and references therein, the question of how to control and stabilize chaotic behaviour in prey-predator systems has been addressed. The dynamics found in such systems strongly depends on compensatory or overcompensatory recruitment.…”

confidence: 99%

“…Moreover, these models also provide efficient computational results for numerical simulations and provide a rich dynamics as compared to the continuous ones [5][6][7][8][9][10]. In the last few years, many interesting papers have appeared in the literature that discuss the stability, bifurcation and chaos phenomena in discretetime models (see [11][12][13][14][15][16][17][18][19][20] and the references cited therein).…”

confidence: 99%