1. A PREDATOR-PREY INTERACTION MODEL WITH SELF- AND CROSS-DIFFUSION IN AQUATIC SYSTEMS.
- Author
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UPADHYAY, RANJIT KUMAR, PATRA, ATASI, DUBEY, B., and THAKUR, N. K.
- Subjects
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AQUATIC ecology , *PREDATION , *COMPUTER simulation , *TURING test , *PREDATORY animals , *PREDATORS of fishes , *MATHEMATICAL models - Abstract
In this paper, the complex dynamics of a spatial aquatic system in the presence of self- and cross-diffusion are investigated. Criteria for local stability, instability and global stability are obtained. The effect of critical wavelength which can drive a system to instability is investigated. We noticed that cross-diffusion coefficient can be quite significant, even for small values of off-diagonal terms in the diffusion matrix. With the help of numerical simulation, we observed the Turing patterns (spots, strips, spot-strips mixture), regular spiral patterns and irregular patchy structures. The beauty and complexity of the Turing patterns are attributed to a large variety of symmetry properties realized by different values of predator's immunity, rate of fish predation and half saturation constant of predator population. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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