6 problems

Let $\mathbf{A}$ be a game matrix and let $\alpha$ be a learning rate. Let $I_G(t)$ denote the relevant maximal-set quantity in the imitation dynamics, and let $\alpha^*$ be a lear…

Let $\mathbf{A}$ be a game matrix and let $\alpha$ be a learning rate. Suppose that the maximal set of $I_G(t)$ is constant for all $t\geq t_0$. Let $\mathcal{X}^*$ denote the maxi…

Let $G$ be a graph, let $K_N$ be the complete graph on $N$ vertices, let $u$ be the all-infected initial infection-probability vector, and let $V_\infty$ be the endemic steady-stat…

Let $G$ be a graph, let $K_N$ be the complete graph on $N$ vertices, let $u$ denote the all-infected initial infection-probability vector, and let $V(0)$ be an initial infection-pr…

Consider networks ${\cal N}_1$ and ${\cal N}_2$ of coupled quadratic nodes. They are in the same uni-asymptotic class when, for every uni-initial condition $z_0\in\mathbb{C}$, the…

Let $n$ interacting agents have opinion vector $x(t)\in\mathbb{R}^n$ and bounds vector $r\in\mathbb{R}^n_{>0}$. In the synchronized bounded confidence (SBC) and synchronized bounde…