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中文摘要：
在Levins模型的基础上研究了色交叉关联噪声对集合种群稳定性的影响,应用Fokker-Plank方程得到了系统的稳态概率密度函数,运用最快下降法得到了平均灭绝时间的解析式.结果表明：两噪声色关联时,加性噪声强度和乘性噪声强度均弱化集合种群的稳定性;噪声关联强度强化集合种群的稳定性.两噪声之间负关联时,平均灭绝时间是加性噪声强度和乘性噪声强度的减函数,是噪声关联时间的增函数;两噪声之间正关联时,平均灭绝时间是加性噪声强度和噪声关联时间乘性噪声强度的减函数,是乘性噪声强度的非单调函数.
英文摘要：
In this paper,the stability for a metapopulation system driven by colored cross-correlated noises is investigated based on the Levins model.The stationary probability distribution and the explicit expression of the mean extinction time are derived according to the Fokker-Planck equation.Numerical results show that in the case of colored correlation between two noises,the addictive noise and the multiplicative noise intensity weaken the stability of metapopulation,and the correlation strength enhances the stability of metapopulation.If the correlation strength between the two noises is negative,the mean extinction time is a decreasing function of intensities of the two noises,but a increasing function of correlation time;if the correlation strength between the two noises is positive,then the mean extinction time is a decreasing function of addictive noise intensity and correlation time,but a non-monotonic function of multiplicative noise intensity.
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