8 problems

The network dynamics use a pumping rate and may involve numerical integration with complex-valued variables. Synchronization-delay conjecture. The synchronization of the network ma…

Let ${\bm{C}}$ be an irreducible row stochastic matrix, and consider the modified/one-step DeGroot–Friedkin model with $r(x)=x$. Stability conjecture. The equilibrium of this model…

Consider the noise-intervened opinion dynamical system described above, with effective noise strength $\delta_2$ and parameter $\epsilon$. Effective-noise-strength conjecture. The…

Let $\rho_1(t)$ denote the fastest convergence rate for the best topologies, and let $n$, $a_{\max}$, and $v$ be the parameters appearing in the protocol and assumptions. Asymptoti…

Let $(F_k,G_k\mid H_k)$ denote the linear discrete-time-varying stochastic system with multiplicative noise considered in the paper. Uniform detectability and ${\cal K}^N$-exact de…

Consider a weakly interacting system of $N$ planets with full dynamics in a $6N$-dimensional phase space, and let $\lambda_1,\ldots,\lambda_{6N}$ denote its Lyapunov exponents. In…

Additive noise can perturb the stability of scalar delayed systems and shift the onset of oscillatory solutions. Noise-induced suppression conjecture. This mechanism might provide…

Consider a noisy linear system with state dynamics $x_{t+1}=Ax_t+Bu_t+w_t$, where the noise has bounded variance and the control input is subject to a positive uniform upper bound…