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Zhang, Huayong; Ma, Shengnan; Huang, Tousheng; Cong, Xuebing; Yang, Hongju; Zhang, Feifan

A new finding on pattern self-organization along the route to chaos. (English) Zbl 1392.39006

Chaos Solitons Fractals 106, 118-130 (2018).
Summary: This research investigates pattern self-organization along the route to chaos in a space- and time-discrete predator-prey system, where the prey shows convection movement in space. Through analysis on Turing instability of the system, pattern self-organization conditions are determined. Based on the conditions, simulations are performed under two initial conditions, demonstrating two pattern transitions along the route to chaos. In the first pattern transition, the patterns start from regular stripes, experiencing twisted stripes, then return to regular stripes again. The second pattern transition is much more complex and shows three stages. Especially, an alternation between ordered patterns and disordered chaos is found, contributing greatly to the spatiotemporal complexity of the system. When the system stays at the homogeneous chaotic states, Turing instability driven by convection and diffusion can still force the self-organization of regular striped patterns. The finding in this research provides a new comprehending for pattern self-organization and transition in spatially extended predator-prey systems.

MSC:

39A14 Partial difference equations
39A12 Discrete version of topics in analysis
37G10 Bifurcations of singular points in dynamical systems
92D25 Population dynamics (general)

Keywords:

self-organization; chaos; predator-prey system; spatiotemporal complexity; Turing instability
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References:

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