Effects of Noises and Habitat Complexity in the Prey-Predator Ecosystem

XU Wei; QI Lu-yuan; GAO Wei-ting

doi:10.3879/j.issn.1000-0887.2013.02.006

Volume 34 Issue 2

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XU Wei, QI Lu-yuan, GAO Wei-ting. Effects of Noises and Habitat Complexity in the Prey-Predator Ecosystem[J]. Applied Mathematics and Mechanics, 2013, 34(2): 162-171. doi: 10.3879/j.issn.1000-0887.2013.02.006

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Effects of Noises and Habitat Complexity in the Prey-Predator Ecosystem

doi: 10.3879/j.issn.1000-0887.2013.02.006

¹Department of Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²Department of Electronic Information, Northwestern Polytechnical University,Xi’an 710129, P.R.ChinaState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University, Changsha 410082, P.R.China;²College of Mechanical and Vehicle Engineering, Hunan University,Changsha 410082, P.R.China

Received Date: 2012-12-17
Rev Recd Date: 2013-01-31
Publish Date: 2013-02-15

Abstract

Abstract

To explore the habitat complexity and random environmental factors effects to the ecosystem, a new stochastic predation type ecosystem with habitat complexity was proposed. Both theoretical analysis and numerical analysis were explored. With the assumption of weak disturbances, the stationary probability density functions (PDF) for both species were obtained by applying the StratonovichKhasminskii averaging principle. The accuracy of the results obtained from theoretical method was demonstrated by those obtained from Monte Carlo simulation (MCS). The system mean first passage time(MFPT) was solved from the Pontryagin equation. The effects of the habitat complexity and the noise intensity were investigated via numerical calculations based on the data obtained from experiment. Results obtained show that: 1) the ecosystem with smaller habitat complexity is less stable when the system is disturbed by noises; 2) the stronger the noise intensities are, the less stable the ecosystem will be; 3) the ecosystem with bigger habitat complexity has longer MFPT; 4) the noise added to the prey natural increase rate has a bigger effect on the MFPT than that added to the predator natural death rate does.
- stochastic ecosystem,
- stationary probability density,
- mean first passage time,
- habitat complexity

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References(24)

References

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