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Segregation Dynamics Motivated by Territorial Markings: The Transition from a Particle to a Continuum Model

Alsenafi, Abdulaziz
http://rave.ohiolink.edu/etdc/view?acc_num=case1467727114

Abstract Details

2016, Doctor of Philosophy, Case Western Reserve University, Applied Mathematics.
We present an agent-based model to simulate gang territorial development motivated by graffiti marking on a two-dimensional discrete lattice. Moreover, we study and analyse the dynamics and steady-state solutions of gang agents and their graffiti markings. For simplicity, we assume that there are only two rival gangs present, and they compete for territory. In this model, agents represent gang members who move according to a biased random walk. All agent interactions are indirect, with the interactions occurring through the graffiti field. Using numerical simulations, we show that gang segregation and territory formation may happen for different system parameters. We also show that a phase transition occurs between a well-mixed state and a segregated state. The numerical results show that the inverse temperature, decay rate and graffiti rate effect the phase transition. From the discrete model, we derive a continuum system for territorial development. Using the continuum equations, we perform a linear stability analysis to determine the stability of the equilibrium solutions. From the results of the linear stability analysis, we show that the critical values of both the discrete model and the continuum system have the same behaviour.
Alethea Barbaro (Advisor)
Erkki Somersalo (Committee Member)
Wanda Strychalski (Committee Member)
Wojbor Woyczynski (Committee Member)
Applied Mathematics; Mathematics

Recommended Citations

Citations

  • Alsenafi, A. (2016). Segregation Dynamics Motivated by Territorial Markings: The Transition from a Particle to a Continuum Model [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1467727114

    APA Style (7th edition)

  • Alsenafi, Abdulaziz. Segregation Dynamics Motivated by Territorial Markings: The Transition from a Particle to a Continuum Model. 2016. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1467727114.

    MLA Style (8th edition)

  • Alsenafi, Abdulaziz. "Segregation Dynamics Motivated by Territorial Markings: The Transition from a Particle to a Continuum Model." Doctoral dissertation, Case Western Reserve University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1467727114

    Chicago Manual of Style (17th edition)

case1467727114
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© 2016, some rights reserved.Creative Commons License Segregation Dynamics Motivated by Territorial Markings: The Transition from a Particle to a Continuum Model by Abdulaziz Alsenafi is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.