TY - GEN
T1 - Feedback Controlled Bifurcation of Evolutionary Dynamics with Generalized Fitness
AU - Dey, Biswadip
AU - Franci, Alessio
AU - Ozcimder, Kayhan
AU - Leonard, Naomi Ehrich
N1 - Publisher Copyright:
© 2018 AACC.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Evolutionary Dynamics
KW - Nonlinear Systems
UR - http://www.scopus.com/inward/record.url?scp=85052579984&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052579984&partnerID=8YFLogxK
U2 - 10.23919/ACC.2018.8431851
DO - 10.23919/ACC.2018.8431851
M3 - Conference contribution
AN - SCOPUS:85052579984
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 6049
EP - 6054
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -