| In this paper,the influence of Gaussian white noise,time delay and periodic signals on the dynamics of population ecosystems have been studied.First,the relative knowledge of random correlation theory in detail in this paper was introduced.Then,based on the small time delay approximation theory and stochastic simulation,the effects of noise and time delay on population dynamics also been analyzed.The results show that:1.For density-dependent invading population model,it is shown that the time delay and noises can cause the regime shifts between low and high population density states.The mean first passage time(MFPT)as a function of noise intensity exhibits a maximum,which identifies the signature of the noise-enhanced stability of the low density state,while the time delay weakens the stability of the low density state.Applying the Kramers time technique,the intersection point of the regime shift time(RST)between low and high population density states also been discuss,i.e.,a critical point in the RST is found.Therefore,the critical point may give an early warning signal of regime shifts from one alternative state to another one for the changes in the noise parameters and time delay.2.For catastrophic damage population ecosystem,the external noise and the positive correlation intensity of the noise can induce the regime shift from the survival state to the extinction state.The negative correlation intensity can induce the the regime shift from the extinction state to the survival state.As the noise intensity changes,the MFPT appears the phenomenon of the noise-enhanced stability of the survival state.And the negative correlation strength can enhance the stability of the survival state,while the positive correlation strength plays a weakening role.The internal and external noise can enhance the response of the system to the input signal.In addition,under the larger negative correlation strength,the system will also appear double stochastic resonance phenomenon. |
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