标题： Mackey-Glass方程中随机共振与随机混沌的共存 显示英文标题

标题： Coexistence of stochastic resonance and stochastic chaos in Mackey-Glass equations

摘要： 我们研究了在噪声存在下的Mackey-Glass方程的动力学行为。 在弱非线性区域，观察到基于确定性吸引子的两个准稳态之间的切换动力学，即随机共振（SR）。 在强非线性区域，我们新发现了具有多个正李雅普诺夫指数的混沌随机共振。 与在弱非线性区域观察到的SR不同，共振点先于最大李雅普诺夫指数的零交叉点出现，导致SR和随机混沌共存。 还基于原点处不稳定螺旋的线性模态分析，提供了弱非线性和强非线性区域中共振周期的精确理论估计。 显示英文摘要

摘要： We investigated the dynamics of the Mackey-Glass equation in the presence of noise. In the weak nonlinearity region, stochastic resonance (SR) is observed as switching dynamics between two quasi-stationary states based on deterministic attractors. In the strong nonlinearity region, we newly discover chaotic SR with multiple positive Lyapunov exponents. Unlike the SR observed in the weak nonlinearity region, the resonance point precedes the zero-crossing point of the largest Lyapunov exponent, resulting in the coexistence of SR and stochastic chaos. A precise theoretical estimation of resonant periods in the weak and strong nonlinearity regions is also provided based on a linear mode analysis of the unstable spiral at the origin.