Bifurcation; Evolutionary Dynamics; Nonlinear Systems; Electrical and Electronic Engineering
Abstract :
[en] Coexistence and interaction of multiple strategies in a large population of individuals can be observed in a variety of natural and engineered settings. In this context, replicator-mutator dynamics provide an efficient tool to model and analyze the evolution of the fractions of the total population committed to different strategies. Although the literature addresses existence and stability of equilibrium points and limit cycles of these dynamics, linearity in fitness functions has typically been assumed. We generalize these dynamics by introducing a nonlinear fitness function, and we show that the replicator-mutator dynamics for two competing strategies exhibit a quintic pitchfork bifurcation. Then, by designing slow-time-scale feedback dynamics to control the bifurcation parameter (mutation rate), we show that the closed-loop dynamics can exhibit oscillations in the evolution of population fractions. Finally, we introduce an ultraslow-time-scale dynamics to control the associated unfolding parameter (asymmetry in the payoff structure), and demonstrate an even richer class of behaviors.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Dey, Biswadip; Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, United States
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; National Autonomous University of Mexico, Department of Mathematics, Mexico City, Mexico
Ozcimder, Kayhan; Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, United States
Leonard, Naomi Ehrich; Princeton University, Department of Mechanical and Aerospace Engineering, Princeton, United States
Language :
English
Title :
Feedback Controlled Bifurcation of Evolutionary Dynamics with Generalized Fitness
Publication date :
09 August 2018
Event name :
2018 Annual American Control Conference (ACC)
Event place :
Milwauke, Usa
Event date :
27-06-2018 => 29-06-2018
Audience :
International
Main work title :
2018 Annual American Control Conference, ACC 2018
Publisher :
Institute of Electrical and Electronics Engineers Inc.
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