کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4497280 | 1318927 | 2011 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Pattern formation and chaos in spatial ecological public goodsgames
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کلمات کلیدی
موضوعات مرتبط
علوم زیستی و بیوفناوری
علوم کشاورزی و بیولوژیک
علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Cooperators and defectors can coexist in ecological public goods games. When the game is played in two-dimensional continuous space, a reaction diffusion model produces highly irregular dynamics, in which cooperators and defectors survive in ever-changing configurations (Wakano et al., 2009. Spatial dynamics of ecological public goods. Proc. Natl. Acad. Sci. 106, 7910-7914). The dynamics is related to the formation of Turing patterns, but the origin of the irregular dynamics is not well understood. In this paper, we present a classification of the spatio-temporal dynamics based on the dispersion relation, which reveals that the spontaneous pattern formation can be attributed to the dynamical interplay between two linearly unstable modes: temporal instability arising from a Hopf-bifurcation and spatial instability arising from a Turing-bifurcation. Moreover, we provide a detailed analysis of the highly irregular dynamics through Fourier analysis, the break-down of symmetry, the maximum Lyapunov exponent, and the excitability of the reaction-term dynamics. All results clearly support that the observed irregular dynamics qualifies as spatio-temporal chaos. A particularly interesting type of chaotic dynamics, which we call intermittent bursts, clearly demonstrates the effects of the two unstable modes where (local) periods of stasis alternate with rapid changes that may induce local extinction.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Theoretical Biology - Volume 268, Issue 1, 7 January 2011, Pages 30-38
Journal: Journal of Theoretical Biology - Volume 268, Issue 1, 7 January 2011, Pages 30-38
نویسندگان
Joe Yuichiro Wakano, Christoph Hauert,