标题： 时间延迟下近双临界Turing-Hopf分支处的空间和时间不稳定性竞争 显示英文标题

标题： Competition of spatial and temporal instabilities under time delay near codimension-two Turing-Hopf bifurcations

摘要： 在接近双临界Turing-Hopf分岔时，研究了时间延迟下空间和时间不稳定性之间的竞争。 时间延迟显著改变了振荡频率、固有波矢量以及Turing模式和Hopf模式的强度。 适当的时间延迟可以控制Turing模式和Hopf模式之间的竞争。 分析表明，单独或两者结合的反馈都可以实现Turing模式和Hopf模式之间转换的控制。 二维数值模拟验证了分析结果。 显示英文摘要

摘要： Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two dimensional numerical simulations validate the analytical results.