CyberSec Research

The complex systems keyword diagram generated by the author in 2010 has been used widely in a variety of educational and outreach purposes, but it definitely needs a major update and reorganization. This short paper reports our recent attempt to update the keyword diagram using information collected from the following multiple sources: (a) collective feedback posted on social media, (b) recent reference books on complex systems and network science, (c) online resources on complex systems, and (d) keyword search hits obtained using OpenAlex, an open-access bibliographic catalogue of scientific publications. The data (a), (b) and (c) were used to incorporate the research community's internal perceptions of the relevant topics, whereas the data (d) was used to obtain more objective measurements of the keywords' relevance and associations from publications made in complex systems science. Results revealed differences and overlaps between public perception and actual usage of keywords in publications on complex systems. Four topical communities were obtained from the keyword association network, although they were highly intertwined with each other. We hope that the resulting network visualization of complex systems keywords provides a more up-to-date, accurate topic map of the field of complex systems as of today.

This paper explores a novel connection between a thermodynamic and a dynamical systems perspective on emergent dynamical order. We provide evidence for a conjecture that Hamiltonian systems with mixed chaos spontaneously find regular behavior when minimally coupled to a thermal bath at sufficiently low temperature. Numerical evidence across a diverse set of five dynamical systems supports this conjecture, and allows us to quantify corollaries about the organization timescales and disruption of order at higher temperatures. Balancing the damping-induced phase-space contraction against thermal exploration, we are able to predict the transition temperatures in terms of the relaxation timescales, indicating a novel nonequilibrium fluctuation-dissipation relation, and formally connecting the thermodynamic and dynamical systems views. Our findings suggest that for a wide range of real-world systems, coupling to a cold thermal bath leads to emergence of robust, non-trivial dynamical order, rather than a mere reduction of motion as in equilibrium.

We demonstrate the deterministic coherence and anti-coherence resonance phenomena in two coupled identical chaotic Lorenz oscillators. Both effects are found to occur simultaneously when varying the coupling strength. In particular, the occurrence of deterministic coherence resonance is revealed by analysing time realizations $x(t)$ and $y(t)$ of both oscillators, whereas the anti-coherence resonance is identified when considering oscillations $z(t)$ at the same parameter values. Both resonances are observed when the coupling strength does not exceed a threshold value corresponding to complete synchronization of the interacting chaotic oscillators. In such a case, the coupled oscillators exhibit the hyperchaotic dynamics associated with the on-off intermittency. The highlighted effects are studied in numerical simulations and confirmed in physical experiments, showing an excellent correspondence and disclosing thereby the robustness of the observed phenomena.

In natural ecosystems and human societies, self-organized resource allocation and policy synergy are ubiquitous and significant. This work focuses on the synergy between Dual Reinforcement Learning Policies in the Minority Game (DRLP-MG) to optimize resource allocation. Our study examines a mixed-structured population with two sub-populations: a Q-subpopulation using Q-learning policy and a C-subpopulation adopting the classical policy. We first identify a synergy effect between these subpopulations. A first-order phase transition occurs as the mixing ratio of the subpopulations changes. Further analysis reveals that the Q-subpopulation consists of two internal synergy clusters (IS-clusters) and a single external synergy cluster (ES-cluster). The former contribute to the internal synergy within the Q-subpopulation through synchronization and anti-synchronization, whereas the latter engages in the inter-subpopulation synergy. Within the ES-cluster, the classical momentum strategy in the financial market manifests and assumes a crucial role in the inter-subpopulation synergy. This particular strategy serves to prevent long-term under-utilization of resources. However, it also triggers trend reversals and leads to a decrease in rewards for those who adopt it. Our research reveals that the frozen effect, in either the C- or Q-subpopulation, is a crucial prerequisite for synergy, consistent with previous studies. We also conduct mathematical analyses on subpopulation synergy effects and the synchronization and anti-synchronization forms of IS-clusters in the Q-subpopulation. Overall, our work comprehensively explores the complex resource-allocation dynamics in DRLP-MG, uncovers multiple synergy mechanisms and their conditions, enriching the theoretical understanding of reinforcement-learning-based resource allocation and offering valuable practical insights

The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for clarifying the dynamical symmetry breaking, it is necessary to use a sufficiently high-precision scheme in the time-dependent framework. Second, the error of numerical calculations is generally more easily accumulated for calculating hyperbolic equations rather than parabolic equations. Third, numerical calculations become easily unstable for nonlinear cases. Our strategy for the high-precision and stable scheme is to implement the implicit Runge-Kutta method for time, and the Fourier spectral decomposition for space. %%% In this paper, focusing on the breather solutions, the relationship between the velocity, mass, and the amplitude of the perturbation is clarified. As a result, the conditions for transitioning from one state to another are clarified.

We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain the formation of such self-organized motifs both on continuous domains or networked systems, where reactions occur in the nodes and the available links are used for species to diffuse. In many relevant applications, those links are not static, as very often assumed, but evolve in time and more importantly they adapt their weights to the states of the nodes. In this work, we make one step forward and we provide a general theory to prove the validity of Turing idea in the case of adaptive symmetric networks with positive weights. The conditions for the emergence of Turing instability rely on the spectral property of the Laplace matrix and the model parameters, thus strengthening the interplay between dynamics and network topology. A rich variety of patterns are presented by using two prototype models of nonlinear dynamical systems, the Brusselator and the FitzHugh-Nagumo model. Because many empirical networks adapt to changes in the system states, our results pave the way for a thorough understanding of self-organization in real-world systems.

Self-organizing systems consume energy to generate internal order. The concept of thermodynamic efficiency, drawing from statistical physics and information theory, has previously been proposed to characterize a change in control parameter by relating the resulting predictability gain to the required amount of work. However, previous studies have taken a system-centric perspective and considered only single control parameters. Here, we generalize thermodynamic efficiency to multi-parameter settings and derive two observer-centric formulations. The first, an inferential form, relates efficiency to fluctuations of macroscopic observables, interpreting thermodynamic efficiency in terms of how well the system parameters can be inferred from observable macroscopic behaviour. The second, an information-geometric form, expresses efficiency in terms of the Fisher information matrix, interpreting it with respect to how difficult it is to navigate the statistical manifold defined by the control protocol. This observer-centric perspective is contrasted with the existing system-centric view, where efficiency is considered an intrinsic property of the system.

The formation of patterns and exotic nonequilibrium steady states in active-fluid systems continues to pose challenging problems -- theoretical, numerical, and experimental -- for statistical physicists and fluid dynamicists. We combine theoretical ideas from statistical mechanics and fluid mechanics to uncover a new type of self-assembled crystal of vortex triplets in an active-spinner fluid. We begin with the two-dimensional Cahn-Hilliard-Navier-Stokes (CHNS) model for a binary-fluid system of active rotors that has two important ingredients: a scalar order parameter field phi that distinguishes regions with clockwise (CW) and counter-clockwise (CCW) spinners; and an incompressible velocity field u. In addition to the conventional CHNS coupling between phi and u, this model has a torque-induced activity term, with coefficient tau, whose consequences we explore. We demonstrate that, if we increase the activity tau, it overcomes dissipation and this system displays a hitherto unanticipated emergent triangular crystal, with spinning vortex triplets at its vertices. We show that this is a nonequilibrium counterpart of an equilibrium plastic crystal. We characterise the statistical properties of this novel crystal and suggest possible experimental realisations of this new state of active matter.

In this paper, we investigate how the internal dynamics of the systems within a network influence the transition to synchronization in adaptive networks of coupled Rossler systems. The network structure is dynamically determined by local energy rules, where links are established according to either intrinsic (conservative) or dissipative energy. By systematically varying one of the system parameter, the bifurcation of an isolated Rossler system illustrates three representative regimes-periodic, multiperiodic, and chaotic-and allows us to study their impact on the collective transition. Our results reveal that the nature of the synchronization transition strongly depends on the interplay between microscopic dynamics and the mesoscopic connectivity structure. Specifically, chaotic oscillators coupled via intrinsic energy exhibit conditions favorable to explosive synchronization, whereas periodic/multiperiodic oscillators consistently yield smooth, continuous transitions. In contrast, dissipative-energy-based connectivity suppresses explosivity in chaotic networks but may induce explosive behavior in multiperiodic systems as network density increases. These findings demonstrate that explosive synchronization is not solely a topological effect but emerges from a nontrivial interaction between local dynamical complexity and temporal network structure. This provides new insight into how internal oscillator states and coupling mechanisms jointly shape the collective organization and dynamic transitions patterns in complex systems.

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the collective dynamics of active self-attracting particles. We identify a sequence of size-controlled transitions that generate characteristic slow modes, leading to exponential increase of patterning timescales. Experimental measurements of multicellular dynamics confirm our predictions.

A machine learning method is proposed using two agents that simulate the biological behavior of a predator and a prey. In this method, the predator and the prey interact with each other - the predator chases the prey while the prey runs away from the predator - to perform an optimization on the landscape. This method allows, for the case of a ravine landscape (i.e., a landscape with narrow ravines and with gentle slopes along the ravines) to avoid getting optimization stuck in the ravine. For this, in the optimization over a ravine landscape the predator drives the prey along the ravine. Thus we also call this approach, for the case of ravine landscapes, the driven hunt method. For some examples of grokking (i.e., delayed generalization) problems we show that this method allows for achieving up to a hundred times faster learning compared to the standard learning procedure.

We present the GRASPion, a compact, open-source bristlebot designed for the controlled study of active matter systems. Built around a low-cost Arduino-compatible board and modular 3D-printed components, the GRASPion combines ease of use, programmability, and mechanical versatility. It features dual vibrating motors for self-propulsion, integrated sensors for local interaction, and customizable firmware enabling various motion modes, from ballistic to diffusive regimes. The robot is equipped with onboard IR communication, color and proximity sensors, and a magnetometer, allowing for real-time interaction and complex collective behaviors. With a runtime exceeding 90 minutes and reproducible fabrication, the GRASPion provides a robust and scalable platform for both educational and research applications in out-of-equilibrium physics. This article details the mechanical and electronic design and software architecture of the GRASPion, and illustrates its capabilities through prototypical experiments relevant to active matter.

This work proposes a hybrid model that combines the Galam model of opinion dynamics with the Bass diffusion model used in technology adoption on Barabasi-Albert complex networks. The main idea is to advance a version of the Bass model that can suitably describe an opinion formation context while introducing irreversible transitions from group B (opponents) to group A (supporters). Moreover, we extend the model to take into account the presence of a charismatic competitor, which fosters conversion back to the old technology. The approach is different from the introduction of a mean field due to the interactions driven by the network structure. Additionally, we introduce the Kolmogorov-Sinai entropy to quantify the system's unpredictability and information loss over time. The results show an increase in the regularity of the trajectories as the preferential attachment parameter increases.

Large Language Models are increasingly used to simulate human opinion dynamics, yet the effect of genuine interaction is often obscured by systematic biases. We present a Bayesian framework to disentangle and quantify three such biases: (i) a topic bias toward prior opinions in the training data; (ii) an agreement bias favoring agreement irrespective of the question; and (iii) an anchoring bias toward the initiating agent's stance. Applying this framework to multi-step dialogues reveals that opinion trajectories tend to quickly converge to a shared attractor, with the influence of the interaction fading over time, and the impact of biases differing between LLMs. In addition, we fine-tune an LLM on different sets of strongly opinionated statements (incl. misinformation) and demonstrate that the opinion attractor shifts correspondingly. Exposing stark differences between LLMs and providing quantitative tools to compare them to human subjects in the future, our approach highlights both chances and pitfalls in using LLMs as proxies for human behavior.

Why do collectives outperform individuals when solving some problems? Fundamentally, collectives have greater computational resources with more sensory information, more memory, more processing capacity, and more ways to act. While greater resources present opportunities, there are also challenges in coordination and cooperation inherent in collectives with distributed, modular structures. Despite these challenges, we show how collective resource advantages lead directly to well-known forms of collective intelligence including the wisdom of the crowd, collective sensing, division of labour, and cultural learning. Our framework also generates testable predictions about collective capabilities in distributed reasoning and context-dependent behavioural switching. Through case studies of animal navigation and decision-making, we demonstrate how collectives leverage their computational resources to solve problems not only more effectively than individuals, but by using qualitatively different problem-solving strategies.

Understanding and predicting the evolution of across complex systems remains a fundamental challenge due to the absence of unified and computationally testable frameworks. Here we propose the Recursive Hierarchical Network(RHN), conceptualizing evolution as recursive encapsulation along a trajectory of node $\to$ module $\to$ system $\to$ new node, governed by gradual accumulation and abrupt transition. Theoretically, we formalize and prove the law of functional evolution, revealing an irreversible progression from structure-dominated to regulation-dominated to intelligence-dominated stages. Empirically, we operationalize functional levels and align life, cosmic, informational, and social systems onto this scale. The resulting trajectories are strictly monotonic and exhibit strong cross-system similarity, with high pairwise cosine similarities and robust stage resonance. We locate current system states and project future transitions. RHN provides a mathematically rigorous, multi-scale framework for reconstructing and predicting system evolution, offering theoretical guidance for designing next-generation intelligent systems.

Natural flocks (aligned) and swarms (non-aligned) both exhibit features of criticality, challenging their treatment as two ends of the same phase transition. We present a model for the cohesion of active individuals, who spontaneously self-assemble into a near-critical state, whether aligned or not. In our framework, these individuals move in open space and possess differing self-propelling velocities. The emerging velocity fluctuations, shown to be correlated and scale-invariant, are triggered by inherent noise rooted in individual imperfections. Using the finite-size scaling theory, we show that our system exhibits criticality features observed in groups of midges and starlings.

Human cooperation persists among strangers despite theoretical predictions of difficulties in large, well-mixed populations, leaving a fundamental evolutionary puzzle. While upstream (pay-it-forward: helping others because you were helped) and downstream (rewarding-reputation: helping those with good reputations) indirect reciprocity have been independently considered as solutions, their joint dynamics in multiplayer contexts remain unexplored. We study N-player giving games with benefit b and cost c and analyze evolutionary dynamics for three strategies: unconditional cooperation (X), unconditional defection (Y), and an integrated reciprocal strategy (Z) combining unconditional forwarding with reputation-based discrimination. We show that integrating upstream and downstream reciprocity can yield a globally asymptotically stable mixed equilibrium of unconditional defectors and integrated reciprocators whenever the benefit-to-cost ratio exceeds a threshold (b/c > 2). Counterintuitively, introducing small complexity costs, rather than destabilizing, stabilizes the equilibrium by preventing not only unconditional cooperators (viewed as second-order freeloaders) but also alternative conditional strategies from invading. While the equilibrium frequency of integrated reciprocators decreases with group size N, it remains positive for any finite N. Rather than requiring uniformity, our model reveals one pathway to stable cooperation through strategic diversity. Defectors serve as "evolutionary shields" preventing system collapse while integrated reciprocators flexibly combine open and discriminative responses. This framework demonstrates how pay-it-forward chains and reputation systems can jointly maintain social polymorphism including cooperation despite cognitive limitations and group size challenges, offering a potential evolutionary foundation for behavioral diversity in human societies.