Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function

Han, Xiaoling; Lei, Ceyu

doi:10.1016/j.chaos.2022.112910

Cited by 19 publications

(3 citation statements)

References 20 publications

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“…Therefore, incorporating the growth of prey based on the proportion of unused available resources into prey reproduction makes the model more realistic from an ecological point of view. In recent years, many mathematical models have been developed to investigate the influence of growth restrictions based on the proportion of available resources on the population structure and ecological diversity [9,10]. Thus,…”

Section: The Modelmentioning

confidence: 99%

“…The authors explored the optimum control strategy of Cydia Pomonella integrated management predator-prey model with Smith growth in [6]. The authors proposed a partial differential predator-prey model with the Smith growth function in [9]. Utilizing the coupled map lattice method, the model transformed into the space-and time-discrete model, and researchers examined the potential of flip bifurcation, Neimark-Sacker bifurcation and Turing bifurcation.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Zhao,

Niu

2024

Mathematics

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The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the population when encountering predators and ignores the role of individual prey. To address this issue, we contemplate the dynamics of a stochastic prey–predator model with Smith growth rate and cooperative defense. The population density of prey is measured by mass, and the growth limitations are based on the proportion of unused available resources. Additionally, the grazing pattern of the predator incorporates cooperative characteristics into the functional response. We carry out existence and uniqueness analysis for the global positive solution. Then, we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solutions for investigating whether prey and predator populations continue to survive. Numerical examples indicate that the Smith growth rate, cooperative defense and environmental disturbance play crucial roles in the coexistence of interacting populations.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Zhao,

Niu

2024

Mathematics

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“…Subsequently, Crowley-Martin [11] and Beddington-DeAngelis [6,12] put forth many functional responses. Subsequently, several studies examined predatorprey models, including several kinds of functional responses [3,4,9,13,17,32,34]. Herd behavior among prey species refers to their tendency to stay together or display similar movement patterns as a protection strategy against predators in the context of predator-prey dynamics.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis of a discrete Leslie predator-prey model with fear effect

Abbas,

Ahmed

2024

VFAST trans. math.

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This study examines a predator-prey model that includes the impact of fear and a square-root functional responseto represent herd behavior in the prey population. Our investigation aims to investigate the existence and stabilityof fixed points in this model. Through conducting an extensive analysis, we have uncovered valuable observations onthe model's behavior, namely recognizing the occurrence of period-doubling and Neimark-Sacker bifurcations.These findings provide an understanding of the intricate dynamics that govern predator-prey interactions in the presence of fear and herd behavior. We provide numerical examples to support our conclusions.

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Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

Lei,

Han,

Wang

2024

Qual. Theory Dyn. Syst.

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Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function

Cited by 19 publications

References 20 publications

Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Stability and bifurcation analysis of a discrete Leslie predator-prey model with fear effect

Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

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