4 problems

Let $\mathcal{V}\in\mathbb{R}^N$ be the vector of intrinsic velocities, and let $\kappa_c(\mathcal{V})$ denote the critical coupling strength of the Winfree system. Let initial dat…

Let $N$ oscillators have initial data $(\{\theta_i^0\}_{i=1}^N,\{\omega_i^0\}_{i=1}^N)$ and system parameters $(\{\nu_i\}_{i=1}^N,\kappa,m)$. Write $\mathcal{V}=(\nu_i)_{i=1}^N$ an…

Let $\Omega=\\{\omega_1,\cdots,\omega_N\\}\in \mathbb{R}^N$ be a fixed frequency vector. Let $\kappa_{\mathrm{c}}(\Omega)$ denote the critical coupling strength for existence of an…

Let $\Omega=\\{\omega_1,\cdots,\omega_N\\}\in \mathbb{R}^N$ be a frequency vector, and let $\Theta^0=\\{\theta_1^0,\cdots,\theta_N^0\\}$ be an initial phase vector. Define the crit…