Transition and resonance induced by colored noises in tumor model under immune surveillance

In this paper, we study stationary probability distribution and stochastic resonance phenomenon in a tumor model under immune surveillance, which is driven by colored Gaussian noises. The signal-to-noise ratio is calculated when periodic signal is introduced. The impacts of self-correlation times 𝜏₁ and 𝜏₂, cross-correlation strength 𝜆 between two noises and time 𝜏₃ on stationary probability distribution and signal-to-noise ratio are discussed, respectively. Research results show that structure of stationary probability distribution transfers from extinction state to tumor stable one as 𝜆, 𝜏₁, 𝜏₂ and 𝜏₃ increase; signal-to-noise ratio as a function of additive noise intensity exhibits maximum and minimum, maximum and minimum are the identifying characteristics of stochastic resonance and stochastic reverse-resonance phenomenon. However for the curve of signal-to-noise ratio as a function of multiplicative noise intensity, there exhibits only a maximum and increases of 𝜆, 𝜏₁ and 𝜏₃ weakens the stochastic resonance and stochastic reverse-resonance; conversely, increase of 𝜏₂ enhances stochastic resonance and stochastic reverse-resonance in tumor model under immune surveillance. (author)