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Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
Attila Szolnoki, Matjaž Perc, 2015, original scientific article

Abstract: If rock beats scissors and scissors beat paper, one might assume that rock beats paper too. But this is not the case for intransitive relationships that make up the famous rock-paper-scissors game. However, the sole presence of paper might prevent rock from beating scissors, simply because paper beats rock. This is the blueprint for the rock-paper-scissors game with protection spillovers, which has recently been introduced as a new paradigm for biodiversity in well-mixed microbial populations. Here we study the game in structured populations, demonstrating that protection spillovers give rise to spatial patterns that are impossible to observe in the classical rock-paper-scissors game.Weshow that the spatiotemporal dynamics of the system is determined by the density of stable vortices, which may ultimately transform to frozen states, to propagating waves, or to target waves with reversed propagation direction, depending further on the degree and type of randomness in the interactions among the species. If vortices are rare, the fixation to waves and complex oscillatory solutions is likelier. Moreover, annealed randomness in interactions favors the emergence of target waves, while quenched randomness favors collective synchronization. Our results demonstrate that protection spillovers may fundamentally change the dynamics of cyclic dominance in structured populations, and they outline the possibility of programming pattern formation in microbial populations.
Keywords: cyclical interactions, pattern formation, vortices, phase transitions, selforganization, biodiversity
Published in DKUM: 03.07.2017; Views: 763; Downloads: 361
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Noise-induced spatial dynamics in the presence of memory loss
Matjaž Perc, Marko Marhl, 2007, original scientific article

Abstract: We study the spatial dynamics of noise-induced waves in two-dimensional excitable media in dependence on the duration of the artificially imposed refractory time that is introduced to each constitutive system unit after an excitation. Due to the introduction of refractory times, a randomly induced spatial wave is temporarily unable to transmit information to the opposite site of its propagation direction. Thus, once the wave leaves the absorbing boundaries of the spatial grid the system has little or no recollection, depending on the duration of the refractory time, of its existence. We show that even in the presence of such memory loss, self-organization of excitatory events leads to noise-induced spatial periodicity in the media. We present a simple analytical treatment of a two-unit system to capture and explain the essence of the observed phenomenon. Since refractory times are widespread in biological systems, our results provide interesting insights into functioning of real-life organisms at the cellular as well as tissue level.
Keywords: noise, spatiotemporal noise, intensity, pattern formation, refractory time, calcium oscillations
Published in DKUM: 07.06.2012; Views: 1658; Downloads: 88
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