RUI - Pattern forming dynamical systems in theory and experiment

Macalester College, Saint Paul MN

Investigators

Abstract

Biological swarms of insects, fish, birds, and other organisms influence ecological and evolutionary dynamics, serve as prototypes for algorithm development of autonomous vehicles, and are rich sources of patterns. Swarms are shaped by an interaction of endogenous social forces with exogenous environmental ones. A kernel describing the social forces is a key element of swarm models. To improve the mathematical understanding of these models, to clarify how exogenous and endogenous forces interact to influence aggregation pattern and morphology, and to provide biological insight into aphids and locusts, we carry out three projects. (1) We analyze and simulate a broadly applicable differential equation based model describing organisms whose movement is due to endogenous and exogenous forces. We connect properties of swarm patterns to properties of the two forces. (2) In experiment, we measure trajectories of pea aphids moving within a group. Using the model from (1), we quantify the social kernel. (3) We generalize the study from (1) by incorporating a dynamically evolving kernel that models social and antisocial behavioral phases in desert locusts. This work will suggest swarm control strategies to minimize aggregation and hence ameliorate some of the negative economic and humanitarian impacts of locust swarms. Turing patterns arise from a competition between reaction and diffusion in diverse chemical, biological, and physical systems. To contribute to the mathematical and chemical understanding of forced patterns, we perform experiments on the chlorine dioxide - iodine - malonic acid (CDIMA) Turing system. Specifically, we force Turing patterns with a time-periodic light source and measure how the resulting pattern suppression scales with forcing parameters. These projects incorporate education through research involvement of twelve undergraduate student researchers, including women, other underrepresented minorities, and post-baccalaureate students bound for graduate study. To forge links between experiment and theory, some students will perform experimental work and all will train within the PI's experimental/theoretical lab. Students will interact with theorists and experimentalists at other universities and undergraduate colleges. Lab and curricular enhancements will provide benefits beyond the term of the grant.