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Emergence of target waves in paced populations of cyclically competing species
Luo-Luo Jiang, Tao Zhou, Matjaž Perc, Xin Huang, Bing-Hong Wang, 2009, original scientific article

Abstract: We investigate the emergence of target waves in a cyclic predator-prey model incorporating a periodic current of the three competing species in a small area situated at the center of a square lattice. The periodic current acts as a pacemaker, trying to impose its rhythm on the overall spatiotemporal evolution of the three species. We show that the pacemaker is able to nucleate target waves that eventually spread across the whole population, whereby three routes leading to this phenomenon can be distinguished depending on the mobility of the three species and the oscillation period of the localized current. First, target waves can emerge due to the synchronization between the periodic current and oscillations of the density of the three species on the spatial grid. The second route is similar to the first, the difference being that the synchronization sets in only intermittently. Finally, the third route toward target waves is realized when the frequency of the pacemaker is much higher than that characterizing the oscillations of the overall density of the three species. By considering the mobility and frequency of the current as variable parameters, we thus provide insights into the mechanisms of pattern formation resulting from the interplay between local and global dynamics in systems governed by cyclically competing species.
Keywords: cyclical interactions, target waves, spatial games, diversity
Published in DKUM: 30.06.2017; Views: 1483; Downloads: 386
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Linearizability conditions of a time-reversible quartic-like system
Xingwu Chen, Wentao Huang, Valery Romanovski, Weinian Zhang, 2011, original scientific article

Abstract: In this paper we study the linearizability problem of polynomial-like complex differential systems. We give a reduction of linearizability problem of such non-polynomial systems to the problem of polynomial systems. Applying this reduction, we find some linearizability conditions for a time-reversible quartic-like complex system and derive from them conditions of isochronous center for the corresponding real system.
Keywords: mathematics, reversibility, isochronous center
Published in DKUM: 07.06.2012; Views: 1436; Downloads: 118
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Quality information and knowledge
Kuan-Tsae Huang, Yang W. Lee, Richard Y. Wang, professional work

Published in DKUM: 01.06.2012; Views: 1522; Downloads: 140
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