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

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.