Effects of periodic force on the stability of the metastable state in logistic system

• Effects of periodic force on the stability of the metastable state in logistic system is investigated.
• When the periodic force takes value of the first half cycle, the stability is weakened by the additive noise.
• When the periodic force takes value of the second half cycle, the stability is enhanced by the additive noise.
• The stability of the metastable state can be controlled with the value of periodic force.

The effects of periodic force on the stability of the metastable state in logistic model are investigated. The expression of the mean first-passage time (MFPT) from the metastable state to the stable state is derived. Based on the expression, the effects of periodic force on the MFPT were analyzed. The results indicate that: (i) For the case of the multiplicative noise induced transition, the multiplicative noise and the periodic force weaken the stability of the metastable state; (ii) For the case of the additive noise induced transition, the stability of the metastable state is weakened by the additive noise when the periodic force takes value of the first half cycle, while the stability of the metastable state is enhanced by the additive noise when the periodic force takes value of the second half cycle; (iii) For the case of the correlation between the multiplicative and the additive noise induced transition, the correlation between the multiplicative and the additive noises and the periodic force weaken the stability of the metastable state.