Scavenger-Predator-Prey Model with Finite Resources

In this dissertation, we present a series of studies that advance the understanding of adaptive behaviors in ecological systems. The thesis is composed of three interconnected works, each delving into the dynamics of predator-prey-scavenger interactions. The first segment of the thesis investigates the role of predator-taxis in pattern formation within predator-prey systems, as documented in the paper ”Generalized Holling III Functional Response: role of predator-taxis on spatial patterns, 2023.” Through a combination of weakly nonlinear analysis and amplitude equations, we delineate the conditions under which subcritical or supercritical Turing bifurcations occur. Our theoretical and numerical findings illuminate the critical influence of predator-taxis coefficients on the emergence of spatial patterns, highlighting their potential as a control parameter in Turing bifurcations. The complexity of pattern formations is further analyzed in the context of cross-diffusion in the second paper, ”Complex Pattern Formations Induced by Cross-Diffusion, 2023.” Here, the interplay of cross-diffusion and habitat complexity is examined, leading to sufficient conditions for Hopf bifurcation and Turing-driven instability. This study provides deep insights into the control parameters that govern pattern formation, offering both theoretical and numerical evidence for diverse and intricate pattern formations, such as spots, stripes, and mixed motifs, which are shaped by cross-diffusion and predator mortality rates. Finally, the thesis presents an ongoing investigation titled ”RL in prey-predator-scavenger with finite resources.” This work aims to integrate the LFA Q-learning framework within a more comprehensive ecological model that includes scavengers, thus broadening the scope of adaptive behaviors and learning mechanisms in the study of ecological systems. By incorporating finite resources and additional agent interactions, this research seeks to unveil new dimensions of ecological dynamics and learning. This dissertation includes material from the articles listed below, which has been included with the permission of my co-authors and in compliance with the respective publishers’ policies: Menacer et al (2024), Souna, Pankaj, Belabess, Menacer (2023)[3] and Souna, Belabess, Menacer (2022).

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2024

Author dc:creator

• Menacer, Youssaf

Committee members dc:contributor.committeemember

• Labate, Demetrio
• Quaini, Annalisa
• Niu, Yabo
• Olsen, Megan

• Ecological systems, Scavenger-predator-prey- interactions, Predator-taxis, Pattern formation, Turing bifurcations, Weakly nonlinear analysis Spatial patterns, Cross-diffusion, Habitat complexity, Hopf bifurcation, Turing-driven instability, Control parameters, Pattern formations, Reinforcement Learning (RL), LFA Q-learning, Finite resources, Ecological dynamics, Ecological model, Learning mechanisms.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10657/17742

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/17742