DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Muruhan Rathinam, Department of Mathematics and Statistics, UMBC

**Title: ***
Convergence, stability and robustness of multidimensional opinion
dynamics in continuous time
*

**Abstract:**
We analyze a continuous time multidimensional opinion model where agents have
heterogeneous but symmetric and compactly supported interaction functions.
We consider Filippov solutions of the resulting dynamics and show strong
Lyapunov stability of all equilibria in the relative interior of the set of
equilibria. For the case of C1 interaction functions, we provide an
alternative proof for the convergence of all trajectories as $t \to \infty$.
We investigate robustness of equilibria when a new agent with arbitrarily
small weight is introduced to the system in equilibrium. Assuming the
interaction functions to be indicators, we provide a necessary condition and
a sufficient condition for robustness of the equilibria.
Our necessary condition coincides with the necessary and sufficient
condition obtained by Blondel et al. for one dimensional opinions.
This is joint work with Serap Tay Stamoulas.

**Time:** Friday, September 16, 2016, 1:30-2:20 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491