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Seminar on mathematical modeling in biology and medicine
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Extensions of Cyclic Competition Models in Population Dynamics Idan Sorin Technion – Israel Institute of Technology, Haifa |
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Abstract: Scissors cut Paper, Paper wraps Rock, and Rock blunts Scissors: the classic game of Rock-Paper-Scissors offers a simple yet compelling model of cyclic dominance. That dynamics is frequently used to illustrate competition between populations or strategies in evolutionary game theory and biology and can be observed in a variety of ecological systems. We consider a Lotka-Volterra model for three competing species, which exhibits periodic solutions associated with a limit cycle. This model can be extended in several ways: via a reaction-diffusion framework, where species move continuously in space, or through a network of habitats, where species disperse between discrete patches. In this talk, we analyze the stability and instability of the periodic solutions in both extensions. Furthermore, we demonstrate the relationship between the stability criteria of these systems and discuss their evolution within the instability regions, showing that the growth of the coupling constant can lead to the desynchronization of oscillations. Language: English |
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