Combined action of time delay and colored cross-correlated Gaussian colored noises on dynamical characteristics for a FitzHugh-Nagumo neural system

In this paper, we focus on the investigation of the regime shift of the steady states, the mean first-passage time (MFPT) and the stochastic resonance (SR) for a FitzHugh-Nagumo neural system with time delay perturbed by colored cross-correlated Gaussian colored noises as well as a periodic signal. By means of a series of numerical calculations, our investigation results show that time delay, the multiplicative noise and the additive one can all produce the negative influence on the maintenance of the stability for the neuronal system; while the two self-correlation times of the internal and external noises, the noise correlation strength and its correlation time can always strengthen the stability of the biological system. As for the MFPT for the FHN system, it is observed that during the recovery process from the excited state to the resting one, we should take measures to increases the noise correlation strength, two noise self-correlation times, and reduce time delay along with the noise correlation time so as to sustain the state of excitation for neuronal cells as far as possible. With respect to the SR phenomenon, it is observed that the noise correlation strength and its correlation time, two Gaussian noise correlation times tau(1), tau(2) can all amplify significantly the SR effect, and even stimulate the double-peaked or three-peaked phenomenon; While time delay and the additive noise will always reduce the SR effect.