Bifurcation analysis of a discrete-time prey-predator model

Abstract

This paper investigates the importance of studying the dynamics of predator-prey systems and the specific significance of Neimark-Sacker and period-doubling bifurcations in discrete-time prey-predator models. By conducting a numerical bifurcation analysis and examining bifurcation diagrams and phase portraits, we present important results that differentiate our study from others in the field. Firstly, our analysis reveals the occurrence of Neimark-Sacker and period-doubling bifurcations in the model under certain parameter values. These bifurcations lead to the emergence of stable limit cycles characterized by complex and unpredictable dynamics. This finding emphasizes the inherent complexity and nonlinearity of predator-prey systems and contributes to a deeper understanding of their dynamics. Additionally, our study highlights the advantages and limitations of employing discrete-time models in population dynamics research. The use of discrete-time models allows for a more tractable analysis while still capturing significant aspects of ecological systems. In conclusion, this study holds importance in shedding light on the dynamics of predator-prey systems and the specific role of Neimark-Sacker and period-doubling bifurcations. Our findings contribute to the understanding of predator-prey systems and offer implications for ecological management strategies.

Stochastic Modeling of Three-Species Prey–Predator Model Driven by Lévy Jump with Mixed Holling-II and Beddington–DeAngelis Functional Responses

“…Certain stochastic prey-predator systems can be established by taking into consideration only the white noise for the studied population [21,22]. Recently, a Brownian random walk perturbation on model (1) was proposed in [20] by studying the persistence and extinction of the prey and predator population. A more basic modification to the modeling technique is to immediately take into account more realistic distributions in order to maintain the model's straightforward analytic form.…”

“…Prey-predator dynamics remain a highly fruitful and attractive ecological subject [1][2][3][4]. The basic prey-predator model was proposed by Lotka and Volterra in 1956 [5]; this basic ecological problem was one of the earliest to model competition between prey and predator.…”

“…where the two prey and one predator populations are presented by X 1 , X 2 , and y, respectively. The parameters of (1) and their meanings are provided in Table 1.…”