A New Approach to Global Stability of Discrete Lotka-Volterra Predator-Prey Models. (1st June 2015)

• Record Type: Journal Article
• Authors: Kim, Young-Hee; Choo, Sangmok
• Other Names: Kon Ryusuke Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-06-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/674027
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : An Euler difference scheme for a three-dimensional predator-prey model is considered and we introduce a new approach to show the global stability of the scheme. For this purpose, we partition the three-dimensional space and calculate the sign of the rate change of population of species in each partitioned region. Our method is independent of dimension and then can be applicable to other dimensional discrete models. Numerical examples are presented to verify the results in this paper.