Research Projects

Coordinated behavior in systems of autonomous agents—such as synchronized flashing in fireflies, flocking in birds, or task-sharing in mobile robot swarms—emerges from the complex interplay of internal rhythms and spatial movement. The concept of swarmalators—agents that move in space while coupling via internal oscillations—has recently emerged as a powerful framework to study such behaviors. However, existing frameworks are often limited in scope: they rely on first-order dynamics and assume metric-based interactions, neglecting the real-world constraints faced by biological and engineered systems. This project fills a critical gap in current models by integrating three key ingredients often ignored: (1) Inertial dynamics, representing the role of mass and momentum in agent motion; (2) Topological interaction rules (e.g., k-nearest neighbors), reflecting limited sensing and processing; (3) External driver agents, modeling purposeful or disruptive influences such as predators, leaders, or external commands. These components are vital for practical applications where agents must respond quickly and coherently under physical constraints and unpredictable perturbations—such as in multi-robot systems, wildlife herds facing threats, or neurons responding to external stimulation. The project addresses two central research problems: • Problem 1: How do inertial and topological interaction rules give rise to coherent spatial and phase structures in undisturbed swarmalator systems? We study how mass, damping, neighborhood size, and phase coupling affect the spontaneous formation and stability of patterns like rotating rings, clusters, and chimera-like states. • Problem 2: How does the presence of external driver agents alter or destabilize synchronization and spatial coordination among swarmalators? We examine how various pursuit strategies, phase-targeting, and feedback rules influence behaviors such as escape, fragmentation, or entrainment. These questions are directly relevant to real-world scenarios: • In swarm robotics, where decentralized agents must avoid collisions, react to moving goals, or escape threats. • In ecological modeling, to understand group responses to predators or environmental stress. • In neuroscience, for developing phase-targeted neuromodulation or brain-machine interfaces. We will derive and analyze second-order coupled differential equations capturing space-phase feedback, use bifurcation and stability tools to identify critical transitions, and run detailed simulations to explore emergent patterns. What makes this work novel and impactful is its unification of biologically and physically realistic features—momentum, limited-range perception, and structured external input—into a coherent dynamical framework. The results will offer not only deeper theoretical insight into complex systems, but also actionable strategies for controlling and designing robust, adaptive, and scalable multi-agent technologies.

Synchronization, Swarming, Swarmalators, Collective motion, Self-organization, Topological Interaction