1. Reputation and reciprocity : reviewChengyi Xia, Juan Wang, Matjaž Perc, Zhen Wang, 2023, review article Abstract: Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higherorder models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.
Keywords: pattern formation, Monte Carlo method, complex network, evolutionary game theory, cooperation, social physics
Published in DKUM: 20.06.2024; Views: 144; Downloads: 7
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2. Turing patterns in simplicial complexesShupeng Gao, Lili Chang, Matjaž Perc, Zhen Wang, 2023, original scientific article Abstract: The spontaneous emergence of patterns in nature, such as stripes and spots, can be mathematically explained by reaction-diffusion systems. These patterns are often referred as Turing patterns to honor the seminal work of Alan Turing in the early 1950s. With the coming of age of network science, and with its related departure from diffusive nearest-neighbor interactions to long-range links between nodes, additional layers of complexity behind pattern formation have been discovered, including irregular spatiotemporal patterns. Here we investigate the formation of Turing patterns in simplicial complexes, where links no longer connect just pairs of nodes but can connect three or more nodes. Such higher-order interactions are emerging as a new frontier in network science, in particular describing group interaction in various sociological and biological systems, so understanding pattern formation under these conditions is of the utmost importance. We show that a canonical reaction-diffusion system defined over a simplicial complex yields Turing patterns that fundamentally differ from patterns observed in traditional networks. For example, we observe a stable distribution of Turing patterns where the fraction of nodes with reactant concentrations above the equilibrium point is exponentially related to the average degree of 2-simplexes, and we uncover parameter regions where Turing patterns will emerge only under higher-order interactions, but not under pairwise interactions.
Keywords: Turing pattern, higher-order network, nonlinear dynamics, pattern formation
Published in DKUM: 31.05.2024; Views: 164; Downloads: 5
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3. Vortices determine the dynamics of biodiversity in cyclical interactions with protection spilloversAttila 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: 1199; Downloads: 417
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4. Noise-induced spatial dynamics in the presence of memory lossMatjaž 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: 2224; Downloads: 97
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