Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems

The emergence of inhomogeneities in the distributions of the abundances of spatially extended prey–predator systems is investigated. The method of analysis, based on the notion of diffusive (Turing) instability, is systematically applied to nine different models obtained by introducing an extra-factor into the standard Rosenzweig–MacArthur prey–predator model. The analysis confirms that the standard model is critical in the context of Turing instability, and that the introduction of any small amount of the extra-factor can easily promote or inhibit the emergence of spatial patterns.

[1]  Zhen Jin,et al.  Predator cannibalism can give rise to regular spatial pattern in a predator–prey system , 2009 .

[2]  Frederic Bartumeus,et al.  MUTUAL INTERFERENCE BETWEEN PREDATORS CAN GIVE RISE TO TURING SPATIAL PATTERNS , 2002 .

[3]  Thilo Gross,et al.  Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. , 2007, Journal of theoretical biology.

[4]  R. Macarthur,et al.  Graphical Representation and Stability Conditions of Predator-Prey Interactions , 1963, The American Naturalist.

[5]  Sergei Petrovskii,et al.  Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system , 2011, Theoretical Ecology.

[6]  Lei Zhang,et al.  Pattern formation of a predator-prey system with Ivlev-type functional response , 2008, 0801.0796.

[7]  Fabio Della Rossa,et al.  Potential Turing instability and application to plant-insect models , 2012, Math. Comput. Model..

[8]  J. McNair,et al.  The effects of refuges on predator-prey interactions: a reconsideration. , 1986, Theoretical population biology.

[9]  Manmohan Singh,et al.  A numerical study of the formation of spatial patterns in twospotted spider mites , 2009, Math. Comput. Model..

[10]  Lei Zhang,et al.  Spatiotemporal complexity of a predator–prey system with constant harvest rate , 2009 .

[11]  G. Ruxton,et al.  Short Term Refuge Use and Stability of Predator-Prey Models , 1995 .

[12]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[13]  L. Segel,et al.  Hypothesis for origin of planktonic patchiness , 1976, Nature.

[14]  J. Beddington,et al.  Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency , 1975 .

[15]  P. Maini,et al.  Turing instabilities in general systems , 2000, Journal of mathematical biology.

[16]  K. McCann,et al.  Food Web Stability: The Influence of Trophic Flows across Habitats , 1998, The American Naturalist.

[17]  J. L. Jackson,et al.  Dissipative structure: an explanation and an ecological example. , 1972, Journal of theoretical biology.

[18]  Johan A. J. Metz,et al.  A size dependent predator-prey interaction: who pursues whom? , 1990 .

[19]  M. Banerjee,et al.  Self-replication of spatial patterns in a ratio-dependent predator-prey model , 2010, Math. Comput. Model..

[20]  Zhen Jin,et al.  Dynamical complexity of a spatial predator-prey model with migration , 2008 .

[21]  G. Ruxton,et al.  Interference and Generation Cycles , 1992 .

[22]  S. L. Lima.  Strong Preferences for Apparently Dangerous Habitats? A Consequence of Differential Escape from Predators , 1992 .

[23]  Zhen Jin,et al.  Spatiotemporal complexity of a ratio-dependent predator-prey system. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.