Dynamics of Collective Decisions in a Time-Dependent Environment
Abstract
The field of dynamical systems had been revolutionized by the seminal work of Leonid Shil'nikov. As a tribute to his genius we analyze in this paper the response of dynamical systems to systematic variations of a control parameter in time, using a normal form approach. Explicit expressions of the normal forms and of their parameter dependences are derived for a class of systems possessing multiple steady-states associated to collective choices between several options in group-living organisms, giving rise to bifurcations of the pitchfork and of the limit point type. Depending on the conditions, delays in the transitions between states, stabilization of metastable states, or on the contrary enhancement of the choice of the most rewarding option induced by the time dependence of the parameter are identified.
