Chaos, Solitons & Fractals

Journal: Chaos, Solitons & Fractals

Publisher

Elsevier

ISSN

0960-0779
1873-2887

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Publications 1 - 10 of 18

Modified particle swarm strategies in spatial public goods games
Gao, Shun; Zhang, Wei; Zhang, Liming; et al. (2025)
Chaos, Solitons & Fractals
Particle swarm optimization (PSO) is a prominent swarm intelligence algorithm where each particle updates its position based on two key components, personal experience (its own historical best solution) and social learning (the best solution found by its neighbors or the swarm). In this study, we enhance both components to propose novel PSO variants. For the personal experience component, we model cognitive bias in self-experience by introducing a biased recollection of individual history, implemented via the Fermi function. Regarding social learning, we incorporate neighbor communication, utilizing either average or optimal neighbor information to guide collective updates. Our results demonstrate that these modifications significantly improve the level of cooperation compared to traditional PSO. By integrating noise-driven decision-making through the Fermi function and employing multi-swarm communication structures, our approach achieves more robust cooperation across diverse environments. These findings underscore the potential of adaptive swarm intelligence principles to foster enhanced cooperation in complex social systems.
Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory
Zhou, Qianli; Deng, Yong (2023)
Chaos, Solitons & Fractals
Graphics with fractal features are usually generated using the Iterated Function System (IFS). IFS can generate the entire family of Sierpinski gaskets by performing different operations on the attractors. As the most classical graphic, Sierpinski gasket can also be generated using mod(n,2). Dempster–Shafer Theory (DST), as a mathematical theory about evidence, models information on the all possible combination states (power set), which relates to 2n. In this paper, we explore the relationship between the Sierpinski gasket and matrix calculus in DST, which is the first time to connect fractal theory and DST from the perspective of geometry. In addition, based on the generation process of the matrices, we propose a method to generate the Sierpinski Gasket using the Kronecker product.
Big data naturally rescaled
Stoop, Ruedi; Kanders, Karlis; Lorimer, Tom; et al. (2016)
Chaos, Solitons & Fractals
Memory-based spatial evolutionary prisoner's dilemma
Xu, Zhixiong; Xu, Zhehang; Zhang, Wei; et al. (2024)
Chaos, Solitons & Fractals
The promotion of cooperation provided by the network, compared to the well-mixed case, strongly depends on the type of strategy-updating mechanism. While many existing theoretical models have focused on agents memorizing neighbors’ strategies, the specific use of memory in representing an individual's resistance to changing their own strategy – and its subsequent impact on the emergence of cooperation – remains underexplored. This study investigates the memory effect on the evolution of cooperation by integrating memory length and strength with the Fermi rule in the evolutionary prisoner's dilemma on a lattice. The Fermi rule incorporates both pairwise interactions and neighborhood interactions. Interestingly, we found the enduring period (END) and the expanding period (EXP) of cooperation, driven by network reciprocity. Notably, players with larger memory sizes exhibit a more pronounced manifestation of this phenomenon. Furthermore, our research highlights that a strong memory strength positively impacts the level of cooperation in the steady state. Additionally, if players prioritize the mean payoff difference among their neighbors over the pairwise difference with a randomly selected player from the neighborhood, it fosters a cooperative environment and enhances the overall level of cooperation. These findings underscore the vital role of memory and local interactions as crucial factors in shaping cooperation dynamics, offering valuable insights for future investigations in this rapidly evolving field.
Network reciprocity and inequality: The role of additional mixing links among social groups
Zhang, Wei (2024)
Chaos, Solitons & Fractals
Local interactions among individuals are often modeled by networks, while global interactions are represented by well-mixed populations. However, people have different roles within their communities, and their interac- tions with family and colleagues are often local and repeated, while interactions with unknown individuals are often global and unpredictable. To capture this situation between local and global interactions, a proposed model studies the effect of additional links that mix local neighborhood and global group interactions. The study aims to evaluate the impact of mixing links on cooperation and inequality. The research found that mixing links can promote the evolution of cooperation, regardless of whether the network is homogeneous (regular random) or heterogeneous (BA scale-free). It also observed that mixing links has a positive effect on upward economic mobility, but they lead to the polarization of wealth. Our research suggests that additional mixing links have a dual nature: improve cooperation and promote upward economic mobility, but widen wealth inequality. Insights offered by this dual-edged nature can be used to understand inequality in interventions of complex social systems.
Power law scaling and "Dragon-Kings" in distributions of intraday financial drawdowns
Filimonov, Vladimir; Sornette, Didier (2015)
Chaos, Solitons & Fractals
Natural data structure extracted from neighborhood-similarity graphs
Lorimer, Tom; Kanders, Karlis; Stoop, Ruedi (2019)
Chaos, Solitons & Fractals
Fractal dimension and image statistics of anal intraepithelial neoplasia
Ahammer, Helmut; Kroepfl, Julia Maria; Hackl, Christoph M.; et al. (2011)
Chaos, Solitons & Fractals
Emerging social brain: A collective self-motivated Boltzmann machine
Tao, Yong; Sornette, Didier; Lin, Li (2021)
Chaos, Solitons & Fractals
Boltzmann machines are unsupervised-learning neural networks, which have contributed to the opening of the field of deep learning architectures. Here we show that, using the modern theory of economic growth, when the number of agents in a free-market society with equal opportunity exceeds a threshold value, a Boltzmann-like income distribution emerges, where the entropy plays the role of swarm intelligence in humans and quantifies its cumulative technological progress. Theoretically, we further show that the emergence of a Boltzmann-like income distribution in a society of optimizing agents reflects the spontaneous organization of a human society to form a Boltzmann machine in which each person plays a role analogous to that of a neuron within a brain-like architecture. This Boltzmann machine exhibits three essential brain-like features, namely the McCulloch-Pitts learning rule, unsupervised-learning, and self-motivation, and satisfies in addition the minimum free-energy principle of the brain theory. Empirically, we investigate the household income data from 66 free-market countries and Hong Kong SAR, and find that, for all of the countries, the income structure for low and middle classes (about 95% of populations) is accurately described by a Boltzmann-like distribution. We suggest that this is a statistical signature that our social networks are going through a critical evolution in the form of a kind of brain-like structure. © 2020 Elsevier Ltd
Strobing brain thunders
Lombardi, F.; Chialvo, D. R.; Herrmann, H. J.; et al. (2013)
Chaos, Solitons & Fractals

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Journal: Chaos, Solitons & Fractals

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