Chaos最新文献

Regarding the issue of protecting ecological resources, this paper establishes a coupled socio-ecological public goods game model to study the impact of dynamic compensation on individual behavior choices and resource evolution. When the compensation intensity is constant, it is found that there is an optimal compensation intensity under different enhancement factors, and the optimal value is negatively correlated with the enhancement factor. The results of the dynamic changes in the compensation intensity indicate that the system has two evolutionary processes: convergence to a stable value and periodic oscillation. Within the steady-state parameter range, a relatively small or large initial compensation intensity can lead the system to a highly vulnerable evolutionary path. Conversely, if sufficient compensation is provided to cooperators at the initial stage, the system will rapidly converge to the stable state of full cooperation. When the initial compensation intensity is moderate, cooperators and defectors coexist. Meanwhile, the greater the enhancement-degradation ratio for compensation intensity, the higher the level of cooperation. In addition, it tends to trigger more significant but slower fluctuations when the response speed of the compensation intensity to the group behavior is relatively slow, whereas a faster response speed leads to higher-frequency fluctuations. Within the parameter range where the system exhibits periodic oscillation, increasing the enhancement-degradation ratio for compensation intensity or the response speed of compensation intensity to group behavior will amplify the amplitude of the system, which is not conducive to the stability of the socio-ecological system.

Institutional punishment is widely used to promote cooperation, yet most existing studies assume that institutions can perfectly identify individual strategies. Under this idealized assumption, cooperators are typically trusted and exempt from monitoring, while sanctions are imposed exclusively on known defectors, thereby neglecting the informational imperfections inherent in real-world governance. To address these limitations, we adopt the zero-trust principle of "never trust, always verify" and develop a zero-trust institutional framework, in which all individuals are subject to uniform monitoring, and sanctions are applied only upon the actual detection of defection. Given that institutional enforcement intensity in practice is rarely static, we further introduce enforcement intensity as an endogenous variable into the Prisoner's Dilemma game and construct a coevolutionary model in which the enforcement intensity and population state are mutually coupled through a closed feedback loop; that is, higher cooperation levels drive the growth of enforcement, while prevalence of defection leads to institutional relaxation. Under fixed and adaptive enforcement intensities, our theoretical and numerical results reveal distinct evolutionary outcomes characterized by different stable equilibria. Finally, by devising the institutional cost functions, we demonstrate that under fixed enforcement, zero-trust punishment outperforms non-zero-trust one in terms of long-run cost-efficiency at intermediate levels of enforcement. Under adaptive zero-trust enforcement, increasing enforcement responsiveness to population state reduces long-run costs when enforcement itself is relatively inexpensive, albeit with diminishing marginal returns, whereas excessive responsiveness increases overall governance costs when enforcement is expensive.

Neuronal systems are highly susceptible to noise, which can trigger erratic, abrupt, and sudden dynamical transitions known as extreme events (EEs). The FitzHugh-Nagumo (FHN) model, a minimal yet powerful two-dimensional representation of neuronal dynamics, has been extensively employed to investigate noise-induced behaviors in both single neurons and monolayer networks. In this work, we extend these studies to a multiplex network consisting of two layers of FHN oscillators with non-local coupling, where each layer is exposed to heterogeneous noise. Our results demonstrate that at low-noise intensities, the probability of EE occurrence increases when neurons exhibit weak synchronization. This weak synchrony acts as a precursor that facilitates the onset of collective firing. However, as the network approaches complete synchrony, the probability of EE decreases sharply and can be entirely suppressed by strengthening the inter-layer coupling. In contrast, at high-noise intensities, EEs disappear in the weakly synchronized regime but re-emerge in the strongly synchronized regime. This reappearance of synchronized EE highlights the critical interplay between noise and coupling. Notably, the observed emergence of EE at both low- and high-noise levels is robust across all coupling ranges from local to global connectivity. These findings provide deeper insight into the mechanisms governing EE generation and neuronal synchronization, offering potential implications for understanding seizure-like dynamics in biological neural systems.

Atopic dermatitis (AD) is a pervasive inflammatory skin disease, with severe forms constituting a refractory phenotype that devastates quality of life through relentless pruritus, widespread lesions, and resistance to standard therapies. A central clinical challenge is to steer the disease away from chronic inflammation and sustain remission. Framed in dynamical terms, this amounts to controlling the remission dynamics of AD. We establish a mathematical framework for the canonical two-phase clinical strategy: the "Get Control" (GC) phase, where antibiotics are administered to suppress acute inflammation, and the "Keep Control" (KC) phase, where emollients are applied to maintain remission. A key question of therapeutic relevance is: what are the minimal drug doses required for each phase to succeed? Our analysis reveals scaling laws that tie the control amplitude (drug dose) directly to two fundamental determinants of severe AD: barrier permeability and immune clearance capacity. These laws delineate the antibiotic dosage required to exit chronic inflammation in GC and the emollient level needed to sustain remission in KC. The uncovered scaling principles elevate treatment design from heuristic to quantitative, leading to a theoretical framework for precision, phase-based analysis of treatment control in severe AD. By aligning clinical intervention with the dynamical structure of the disease, the framework points toward personalized, optimally dosed strategies for overcoming refractory cases.

How does quantum chaos lead to rapid scrambling of information as well as systematic errors across a system when one introduces perturbations in the dynamics? What are its consequences for the reliability of quantum simulations and quantum information processing? We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. We construct a quantity to capture the scrambling of systematic errors, an out-of-time-ordered correlator (OTOC), which serves as a signature of chaos and quantifies the spread of errors. We show that the spread of errors, as quantified by the OTOC, is related to the operator Loschmidt echo, which is defined as the Hilbert-Schmidt inner product of the operators On, and O'n generated from repeated application of the Floquet map for ideal (unperturbed) dynamics and the true (perturbed) dynamics, respectively. This also gives us an operational interpretation of Loschmidt echo (LE) for operators by connecting it to the performance of quantum tomography. We show how our results demonstrate not only a link between LE and scrambling of errors different than previous studies, but also that such a link can have operational consequences in quantum information processing.

Explosive synchronization (ES), which was observed in the scale-free network of the Kuramoto model [J. Gómez-Gardeñes et al., Phys. Rev. Lett. 106, 128701 (2011)], has been studied widely in the oscillator model. However, investigations of ES in neuronal networks, in spite of their importance in neuroscience, are limited and restricted to specific models. In this work, we explore the nature of the transition to synchronization in a class of neurons, namely, type-I neurons. Leveraging the mapping between networks of weakly heterogeneous type-I neurons and the Kuramoto model [P. Clusella et al., Chaos 32, 013105 (2022)] under weak coupling, we investigate whether the conditions known to induce ES in the Kuramoto model also do so in type-I neurons. The neurons are coupled through electrical synapses and placed on scale-free and star networks with complete and partial degree-frequency correlation conditions. Our simulations show ES in networks of Quadratic Integrate and Fire (QIF) neurons, the normal form of type-I neurons close to saddle node on invariant circle (SNIC) bifurcation, under weak heterogeneity. We further generalize this phenomenon to networks of type-I Morris-Lecar neurons, under conditions similar to those of QIF neurons. Thus, this work suggests conditions under which ES can arise in type-I neurons close to SNIC bifurcation under weak heterogeneity and weak electrical coupling.

Misinformation is pervasive in natural, biological, social, and engineered systems, yet its quantitative characterization remains challenging due to context-dependent errors and the heterogeneous structure of real-world interaction networks. We develop a general mathematical framework for quantifying information distortion in distributed systems by modeling how local transmission errors accumulate along network geodesics and reshape each agent's perceived global state. Through a drift-fluctuation decomposition of pathwise binomial noise, we derive closed-form expressions for node-level perception distributions and show that directional bias induces only a uniform shift in the mean, preserving the fluctuation structure. This establishes a previously unreported shift-invariance principle governing error propagation in networks. Applying the framework to canonical graph ensembles, we uncover strong topological signatures of misinformation: Erdős-Rényi random graphs exhibit a double-peaked distortion profile driven by connectivity transitions and geodesic-length fluctuations, scale-free networks suppress misinformation through hub-mediated integration, and optimally rewired small-world networks achieve comparable suppression by balancing clustering with short paths. A direct comparison across regular lattices, Erdős-Rényi random graphs, Watts-Strogatz small-world networks, and Barabási-Albert scale-free networks reveals a connectivity-dependent crossover. In the extremely sparse regime, scale-free and Erdős-Rényi networks behave similarly. At intermediate sparsity, Watts-Strogatz small-world networks exhibit the lowest misinformation. In contrast, Barabási-Albert scale-free networks maintain low misinformation in sparse and dense regimes, while regular lattices produce the highest distortion across connectivities. We additionally show how sparsity constraints, structural organization, and connection costs delineate regimes of minimal misinformation. Overall, our results provide an analytically tractable foundation for understanding and controlling information reliability in complex networked systems.

By extending Takens' embedding theorem [Dynamical Systems and Turbulence, Warwick 1980, edited by D. Rand and L.-S. Young (Springer, Berlin, 1981), pp. 366-381], Deyle and Sugihara [PLoS One 6, 1-8 (2011)] provided a theoretical justification for using parallel measurement time series to reconstruct a system's attractor. Building on Takens' framework, Brunton et al. [Nat. Commun. 8, 19 (2017)] introduced the Hankel alternative view of Koopman (HAVOK) algorithm, a data-driven approach capable of linearizing chaotic systems through delay embeddings. In this work, a modified version of the original algorithm (mHAVOK) is presented, a practical realization of Deyle and Sugihara's generalized embedding theory. mHAVOK extends the original algorithm from one to multiple input time series and introduces a systematic approach to separating linear and nonlinear terms. An R2-informed quality score is introduced and shown to be a reliable guide for the selection of the reduced rank. The algorithm is tested on the familiar Lorenz system, as well as the more sophisticated Sprott system, which features different behaviors depending on the initial conditions. The quality of the reconstructions is assessed with the Chamfer distance, validating how mHAVOK allows for a more accurate reconstruction of the system dynamics. The new methodology generalizes HAVOK by allowing the analysis of multivariate time series, fundamental in real-life data-driven applications.

In this paper, we first develop a deterministic susceptible-infected-quarantined-recovered-susceptible epidemic model with nonlinear incidence rate and investigate the global stability of the equilibria of the model. Then, we extend the deterministic model to a stochastic framework by introducing the lognormal Ornstein-Uhlenbeck process to model the inherent randomness of the disease transmission. Following that, we analyze the stochastic dynamics of the model in detail. More precisely, by adopting the Markov semigroup theory and Lyapunov function techniques, we first establish sufficient criteria for the existence and uniqueness of an invariant probability measure of the model when the parameter R0S>1, indicating the strong persistence of the disease. Afterward, under the same conditions as the global stability of the endemic equilibrium, we achieve the concrete form of the local probability density function near the quasi-endemic equilibrium of the stochastic model. Simultaneously, we also show that the invariant global probability density function can be approximated by the local probability density function when the noise intensity approaches zero. Subsequently, sufficient criteria for disease extinction are presented when the parameter R0S<1. Crucially, we obtain the threshold that determines the outbreak or extinction of the disease. Finally, several examples together with comprehensive numerical simulations are performed to confirm our analytical findings.