Flow-Kick Dynamics in Population Biology: Bridging Continuous and Discrete Processes

Organizers:

Sebastian Schreiber (University of California, Davis)

Description:

This minisymposium will explore recent advances in flow-kick (aka hybrid or impulsive) dynamical systems and their applications to population biology. Flow-kick models, which combine continuous dynamics with discrete perturbations of states and parameters, provide a powerful framework for studying biological systems that experience both smooth and abrupt changes. Recent theoretical developments have established new tools for analyzing the interplay between continuous and discrete processes in biological systems. Applications including consumer-resource dynamics with seasonal reproduction, epidemiological models with pulsed vaccination, and population management with periodic harvesting demonstrate how flow-kick approaches can capture emergent phenomena missed by purely continuous or discrete models. The minisymposium will bring together researchers developing mathematical theory and numerical methods for flow-kick systems alongside those applying these tools to concrete biological problems. Talks will showcase both analytical approaches and empirical applications, with emphasis on mechanistic understanding of population responses to perturbation. By highlighting this growing synthesis of theory and application, the session aims to stimulate new collaborations advancing our ability to understand and manage populations experiencing recurrent disturbances.

Diversity Statement:

Our minisymposium 'Flow-Kick Dynamics in Population Biology' demonstrates diversity across multiple dimensions. The speakers represent gender parity (50%% women), varied career stages (from graduate students to full professors), diverse institution types (from undergraduate colleges to research universities), and broad geographic representation across North America. This diversity strengthens our exploration of flow-kick dynamics in population biology.