标题： 随机Mackey-Glass方程中的共振和混沌 显示英文标题

标题： Resonance and chaos in the stochastic Mackey-Glass equation

摘要： 本研究关注随机Mackey-Glass方程中的噪声诱导现象。在弱非线性区域，观察到具有负最大Lyapunov指数的两个点、周期和混沌吸引子之间的标准随机共振（SRs）切换。数值计算得到的共振周期偏离了基于时间延迟的经典估计，我们提供了更精确的估计，基于现有不稳定螺旋的线性模式分析。在强非线性区域，我们新发现了具有多个正Lyapunov指数的高维混沌SR，这之前未被报道过。与弱非线性区域的动力学不同，共振点先于最大Lyapunov指数的零交叉点出现，导致高维随机混沌和SR的同时存在。 显示英文摘要

摘要： The study focuses on noise-induced phenomena in stochastic Mackey-Glass equations. In the weak nonlinearity region, the standard stochastic resonances (SRs) switching between two point, periodic, and chaotic attractors are observed with the negative largest Lyapunov exponent. The numerically computed resonant period deviates from the classical estimation based on time delays and we provide a more precise estimation based on a linear mode analysis of the existing unstable spiral. In the strong nonlinearity region, we newly discover high-dimensional chaotic SR with multiple positive Lyapunov exponents, which has not been previously reported. Unlike the dynamics in the weak nonlinearity region, the point of resonance precedes the zero-crossing point of the largest Lyapunov exponent, resulting in the coexistence of high-dimensional stochastic chaos and SR.