Hopf Bifurcation in a Predator-Prey Model With Memory Effect and Intra-Species Competition in Predator

Jin, Dayong; Yang, Ruizhi

doi:10.11948/20220127

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…However, various mathematical model options can be explored for future investigations. Potential directions for model development include a difference model [36][37][38], fractional difference [39,40], fractional differential [41,42], and partial differential [43][44][45]. Given that the data obtained in applications are discrete in time, the inclusion of a difference- Srinivas et al [24] developed a mathematical model for predator-prey dynamics in marine reserves and harvesting areas considering both immature and mature predator species.…”

Section: 𝐸 (𝑢) = 𝛼 (𝑡) − 𝛽 (𝑡)mentioning

confidence: 99%

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

et al. 2023

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The United Nations has predicted the growth of the human population to reach 8.405 billion by mid-2023, which is a 70% increase in global food demand. This growth will significantly affect global food security, mainly marine resources. Most marine resources exist within complex biological food webs, including predator–prey interactions. These interactions have been researched for decades by mathematicians, who have spent their efforts developing realistic and applicable models. Therefore, this paper systematically reviews articles related to predator–prey models considering the harvesting of resources in marine protected areas. The review identifies future remodeling problems using several mathematical tools. It also proposes the use of feedback linearization consisting of both the approximation and exact methods as an alternative to Jacobian linearization. The results show that in an optimal control analysis, adding a constraint in the form of population density greater than or equal to the positive threshold value should be considered to ensure an ecologically sustainable policy. This research and future developments in this area can significantly contribute to achieving the Sustainable Development Goals (SDGs) set for 2030.

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Section: 𝐸 (𝑢) = 𝛼 (𝑡) − 𝛽 (𝑡)mentioning

confidence: 99%

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

et al. 2023

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Dynamics in a predator-prey model with predation-driven Allee effect and memory effect

Zhang,

Jin

2024

Open Mathematics

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In this article, a diffusive predator-prey model with memory effect and predation-driven Allee effect is considered. Through eigenvalue analysis, the local asymptotic stability of positive constant steady-state solutions is analyzed, and it is found that memory delay affects the stability of positive constant steady-state solutions and induces Hopf bifurcation. The properties of Hopf bifurcating periodic solutions have also been analyzed through the central manifold theorem and the normal form method. Finally, our theoretical analysis results were validated through numerical simulations. It was found that both memory delay and predation-driven Allee effect would cause the positive constant steady-state solution of the model to become unstable, accompanied by the emergence of spatially inhomogeneous periodic solutions. Increasing the memory period will cause periodic oscillations in the spatial distribution of the population. In addition, there would also be high-dimensional bifurcation such as Hopf–Hopf bifurcation, making the spatiotemporal changes of the population more complex.

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Hopf Bifurcation in a Predator-Prey Model With Memory Effect and Intra-Species Competition in Predator

Cited by 2 publications

References 26 publications

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Dynamics in a predator-prey model with predation-driven Allee effect and memory effect

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