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This page is devoted to the joint research project between Irina Popovici and Constantine Medynets on swarming dynamical and more general autonomous systems. The projected is supported by the Office of Naval Research Grant #N0001421WX00045.
SLIDES: ONR Nonlinear Physics, 2022, keynote, powerpoint, pdf
OUR Research InTERESTS include
OUR Research InTERESTS include
Development of mathematical methods for dimension reduction, control, and stability analysis
Classification of rare dynamical events occurring in these systems Error analysis
Data-driven classifications of dynamical mode
Stability Theory of Dynamical Systems
Areas of applications include: network synchronization, adversary swarm capturing, swarm control, optimal sensor placements (biochemical defense)
Publications
Publications
On Spatial Cohesiveness of Second-Order Self-Propelled Multi-Particle Systems 2023, download pdf
On the Stability of Rotating States in Second-Order Self-Propelled Swarming Systems, 2023, download pdf
Animations
Animations
Paper "On the Stability of Rotating States in Second-Order Self-Propelled Multi-Particle Systems"
Paper "On the Stability of Rotating States in Second-Order Self-Propelled Multi-Particle Systems"
Parabolic Potent Mixed State n=3 with trajectories ftime = 100.mp4Animation. 1. A mixed state: The center of mass (the red dot) is not stationary.
Parabolic Potent Transl State n=60 ftime = 100.mp4Animation 2. A translating state: The center of mass moves along a straight line with a unit speed. The agents stay within a bounded distance of the center of mass.
Parabolic Potential ring State.mp4Animation 3. A ring state. Convergence towards a ring state. A ring state is a configuration when the center of mass is stationary, the agents stay on the unit circle and rotate with a unit speed about the center of mass.
Parabolic Potent Two Groups converging to nondegerate nAgents = 20 ver 2.mp4Animation 4. A ring state. A group of 20 agents are split up into two groups that eventually convergence towards a ring state.
Parabolic Potent Collapsing Group nAgents = 20.mp4Animation 5. A degenerate ring state. A degenerate ring state is characterized as a rotation with agents forming two polar-opposite groups. Two groups of agents with 10 agents per group. One group of 10 agents have identical initial conditions and such as they are represented by one point. Our theory predicted that the second group of agents will also converge to a point. The speed of convergence to a degenerate ring state is very slow, about 1/Sqrt[t]. We had to speed up the time to shorter the video.
Parabolic Potent Collapsing Group Combined nAgents = 20 ver 2.mp4Animation 6. A degenerate ring state. We present the same simulation as in Animation 5, but we stop the rotation and speed up the time to illustrate the convergence to a degenerate ring state.
ON SPATIAL COHESIVENESS OF SECOND-ORDER SELF-PROPELLED SWARMING SYSTEMS
ON SPATIAL COHESIVENESS OF SECOND-ORDER SELF-PROPELLED SWARMING SYSTEMS
In the paper, we study the model with generalized coupling. The matrix A = {a_{k,m}} is symmetric and nonnegative definite.
Generalized Coupling Matrix nAgents 60.mp4Animation 1. A limit state of the generalized model. The limit state can be viewed as the generalized ring state. The matrix A = I-Q, where Q is a projection matrix on some one-dimensional subpace of R^n.
Generalized Coupling Matrix with Circles nAgents 60.mp4Animation 2. The dynamics on the left seems chaotic. However, upon closer examination, one can see that the agents rotate with unit speed about some fixed points. These stationary turn out to be the geometric centers of the form Sum_{m}a_{k,m}r_m
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