13 citations · 23 across the 7 of their papers we have counts for
7 papers
Oscillatory Instabilities of a One-Spot Pattern in the Schnakenberg Reaction-Diffusion System in -D Domains
Siwen Deng, Justin Tzou, Shuangquan Xie
For an activator-inhibitor reaction-diffusion system in a bounded three-dimensional domain of volume and small activator diffusivity of , we employ a h…
Localized patterns in the Gierer Meinhardt model on a cycle graph
Theodore Kolokolnikov, Juncheng Wei, Shuangquan Xie
In this study, we provide a detailed analysis of the spike solutions and their stability for theGierer-Meinhardt model on discrete lattices. We explore several phenomena that have…
Dynamics of N-spot rings with oscillatory tails in a three-component reaction-diffusion system
Yasumasa Nishiura, Shuangquan Xie
In two-dimensional space, we investigate the slow dynamics of multiple localized spots with oscillatory tails in a specific three-component reaction-diffusion system, whose key fea…
Complex oscillatory motion of multiple spikes in a three-component Schnakenberg system
Shuangquan Xie, Theodore kolokolnikov, Yasumasa Nishiura
In this paper, we introduce a three-component Schnakenberg model. Its key feature is that it has a solution consisting of N spikes that undergoes a Hopf bifurcation with respect to…
Multi-vortex crystal lattices in Bose-Einstein Condensates with a rotating trap
Shuangquan Xie, Panayotis G. Kevrekidis, Theodore Kolokolnikov
We consider vortex dynamics in the context of Bose-Einstein Condensates (BEC) with a rotating trap, with or without anisotropy. Starting with the Gross-Pitaevskii (GP) partial diff…
Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates
P. G. Kevrekidis, Wenlong Wang, R. Carretero-Gonzalez +2
We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of th…
Drunken robber, tipsy cop: First passage times, mobile traps, and Hopf bifurcations
Justin C. Tzou, Shuangquan Xie, Theodore Kolokolnikov
For a random walk on a confined one-dimensional domain, we consider mean first passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile tr…