Pattern formation in a space- and time-discrete predator–prey system with a strong Allee effect |
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Authors: | Luiz Alberto Díaz Rodrigues Diomar Cristina Mistro Sergei Petrovskii |
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Institution: | 1.Departamento de Matemática,Universidade Federal de Santa Maria,Santa Maria,Brazil;2.Department of Mathematics,University of Leicester,Leicester,UK |
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Abstract: | The spatiotemporal dynamics of a space- and time-discrete predator–prey system is considered theoretically using both analytical
methods and computer simulations. The prey is assumed to be affected by the strong Allee effect. We reveal a rich variety
of pattern formation scenarios. In particular, we show that, in a predator–prey system with the strong Allee effect for prey,
the role of space is crucial for species survival. Pattern formation is observed both inside and outside of the Turing domain.
For parameters when the local kinetics is oscillatory, the system typically evolves to spatiotemporal chaos. We also consider
the effect of different initial conditions and show that the system exhibits a spatiotemporal multistability. In a certain
parameter range, the system dynamics is not self-organized but remembers the details of the initial conditions, which evokes
the concept of long-living ecological transients. Finally, we show that our findings have important implications for the understanding
of population dynamics on a fragmented habitat. |
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