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Persistence in predator-prey systems with ratio-dependent predator influence

โœ Scribed by H. I. Freedman; R. M. Mathsen

Book ID
112754282
Publisher
Springer
Year
1993
Tongue
English
Weight
555 KB
Volume
55
Category
Article
ISSN
1522-9602

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๐Ÿ“œ SIMILAR VOLUMES

Persistence in predator-prey systems wit
Persistence in predator-prey systems with ratio-dependent predator influence
โœ H.I. Freedman; R.M. Mathsen ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Springer ๐ŸŒ English โš– 567 KB

Predator-prey models where one or more terms involve ratios of the predator and prey populations may not be valid mathematically unless it can be shown that solutions with positive initial conditions never get arbitrarily close to the axis in question, i.e. that persistence holds. By means of a tran

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โœ Dipak Kesh; A. K. Sarkar; A. B. Roy ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 95 KB ๐Ÿ‘ 1 views

In this study, we consider a mathematical model of two competing prey and one predator system where the prey species follow Lotka}Volterra-type dynamics and the predator uptake functions are ratio dependent. We have derived the conditions for existence of di!erent boundary equilibria and discussed t

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A ratio-dependent predatorโ€“prey model with diffusion
โœ Xianzhong Zeng ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 281 KB

This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator-prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists a 0 (b) satisfying 0 < a 0 (b) < m 1 for 0 < b < m 1 , suc

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โœ Xiaoquan Ding ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 170 KB

By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solutions in generalized ratio-dependent predator-prey systems. Some known results are shown to be special cases of the presented paper.