AI 中文总结
本文研究了以Wentzell边界条件耦合的两个标量动力学系统的动力学行为，通过数值延拓分析分岔与稳定性，拓展了单系统耦合延迟的研究，为生物膜建模提供理论支撑。
AI 中文摘要
本文研究了两个相同的标量动力学系统通过标量扩散方程耦合的问题，涉及从对称稳态到对称和非对称稳态的分岔，以及同相和反相振荡的分岔。基于所建立理论的数值延拓方法展示了分岔分支的形状，以及远离分岔起始时的吸引非线性态，并在很大程度上证实了这些态的稳定性。本研究拓展了关于单个标量动力学系统通过相邻扩散场与其自身延迟耦合的动力学性质的工作，进一步量化了两个此类Wentzell边界之间扩散信息传输的延迟。该数学系统的研究动机是对生物膜进行建模，生物膜具有尚未明确的有效局部通量，这些通量与体扩散相耦合。
英文摘要
Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and asymmetric steady-states and to in-phase and anti-phase oscillations. Numerical continuations based on the developed theory show the shape of the bifurcation branches and the attracting nonlinear states far from bifurcation onset and confirm their, for the most part, derived stability. This study extends the work on the dynamical properties of a single scalar dynamical system coupled to its own delay through an adjacent diffusion field and quantifies further the delay of diffusive information transmission between two such Wentzell boundaries. The mathematical system is motivated by modeling biological membranes with yet unknown effective local fluxes that are coupled to bulk diffusion.
Comments38 pages, 10 figures, submitted to the European Journal of Applied Mathematics
