Predator-Prey Interactions: Insights into Allee Effect Subject to Ricker Model
M. Y. Hamada,
Tamer El-Azab,
H. El-Metwally
Issue:
Volume 12, Issue 4, August 2023
Pages:
59-71
Received:
16 May 2023
Accepted:
19 July 2023
Published:
25 September 2023
Abstract: This study investigates the dynamic properties of a discrete predator-prey model influenced by the Allee effect. Through rigorous analysis utilizing bifurcation theory and the center manifold theorem, we establish the stability of the system’s local equilibrium and reveal the intricate dynamical behaviors exhibited by the model, including period-doubling bifurcations at periods 2, 4, and 8, as well as the emergence of quasi-periodic orbits and chaotic sets. A notable finding is the significant role played by the parameter r in shaping the system’s behavior, as we identify a series of bifurcations, such as flip and Neimark-Sacker bifurcations, by systematically varying r while keeping other parameters fixed. These findings underscore the non-linear nature of the model and provide valuable insights into its complex dynamics. Our enhanced understanding of these bifurcations and resulting dynamical behaviors deepens our knowledge of the Allee effect’s implications for predator-prey models, contributing to our comprehension of population oscillations, stability transitions, and the emergence of chaotic dynamics in ecological systems under the Allee effect. Moreover, this study carries practical implications for population management and conservation strategies, as incorporating the Allee effect into predator-prey interactions allows for better insights into population dynamics and the development of more effective and sustainable management practices. Overall, this comprehensive analysis of the discrete predator-prey model under the Allee effect uncovers intricate dynamical behaviors and emphasizes the influential role of the parameter r in shaping system dynamics, with implications for both theoretical understanding and practical conservation management strategies.
Abstract: This study investigates the dynamic properties of a discrete predator-prey model influenced by the Allee effect. Through rigorous analysis utilizing bifurcation theory and the center manifold theorem, we establish the stability of the system’s local equilibrium and reveal the intricate dynamical behaviors exhibited by the model, including period-do...
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Some Fixed Point Theorems on b2 - Metric Spaces
Bheem Singh Patel,
Zaheer Kareem Ansari,
Dharmendra Kumar,
Arun Garg
Issue:
Volume 12, Issue 4, August 2023
Pages:
72-78
Received:
25 August 2023
Accepted:
14 September 2023
Published:
27 September 2023
Abstract: In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a generalization of 2-metric space. The purpose of this research article to established some results of 2-metric space proved by the Arun Garg et al. in b2 -metric spaces and prove new results.
Abstract: In this study, we generalize both b-metric spaces and 2-metric spaces into a new class of generalized metric spaces that we call b2-metric spaces. Then, under various contractive circumstances in partially ordered spaces, we demonstrate a few fixed point theorems in b2-metric space. Many Mathematician gave the concept of b2 -metric spaces as a gene...
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