Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics

<p style='text-indent:20px;'>We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function coupling strength function. The model(CWM) is an integro-differential equation for temporal evolution phase field. LWM describes synchronous behavior weakly coupled oscillators lying in compact region. For bounded measurable initial field, we establish global well-posedness classical solutions to CWM under suitable assumptions function, also show that solution can be obtained <inline-formula><tex-math id="M1">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>-limit sequence solutions. Moreover, presence frustration effect, stationary states bump emerge from some admissible class data large intermediate regimes, respectively. We provide several numerical examples compare them with analytical results.</p>