Chaos最新文献

The study of Turing patterns has been successfully extended from continuous media to single-layer and, more recently, multigraph networks. However, analyzing Turing instability in multigraph networks remains a challenge, as the existing approximate method relies on restrictive assumptions about dense-network connectivity. To address this limitation, we propose a novel least squares framework by reformulating the stability analysis as an optimization problem, leading to improved approximate conditions for Turing instability in multigraph networks. We validate our framework through numerical simulations, demonstrating its superior effectiveness, particularly in networks with Poisson degree distributions where prior methods fail. More than an analytical tool, this framework is leveraged to showcase how to design Laplacian spectra of a network family to drive Turing instability. Furthermore, we develop greedy algorithms for targeted modifications of edges to induce Turing instability. This work provides a versatile theoretical tool and opens new avenues for engineering pattern formation in multi-layer systems.

This paper surveys the profound impact of Serge Aubry's work on mathematics, particularly in Hamiltonian dynamical systems. We trace the historical development from Newtonian mechanics through the Kolmogorov-Arnold-Moser theory to Aubry's groundbreaking contributions to the Aubry-Mather theory, Aubry-André duality, anti-integrability, and their applications across physics and mathematics.

Stochastic resonance (SR) manifests as switching dynamics between two quasi-stationary states in the stochastic Mackey-Glass equation. We identify chaotic SR, arising from the coexistence of resonance and chaos in stochastic dynamics. In contrast to classical SR, which is described by a random point attractor with a negative largest Lyapunov exponent, chaotic SR is described by a random strange attractor with a positive largest Lyapunov exponent. We observe chaotic SR in the Mackey-Glass equation as well as chaotic SR in the Duffing equation and the underdamped FitzHugh-Nagumo equation, demonstrating the universality of this phenomenon across a broad class of strongly nonlinear random dynamical systems.

Natural birth and death are fundamental mechanisms of population dynamics in ecosystems and have played pivotal roles in shaping population dynamics. Nevertheless, in studies of cyclic competition systems governed by the rock-paper-scissors (RPS) game, these mechanisms have often been ignored in analyses of biodiversity. On the other hand, given the prevalence and profound impact on biodiversity, understanding how higher-order interactions (HOIs) can affect biodiversity is one of the most challenging issues, and thus, HOIs have been continuously studied for their effects on biodiversity in systems of cyclic competing populations, with a focus on neutral species. However, in real ecosystems, species can evolve and die naturally or be preyed upon by predators, whereas previous studies have considered only classic reaction rules among three species with a neutral, nonparticipant species. To identify how neutral species can affect the biodiversity of the RPS system when species' natural birth and death are assumed, we consider a model of neutral species in higher-order interactions within the spatial RPS system, assuming birth and death processes. Extensive simulations show that when neutral species interfere positively, they dominate the available space, thereby reducing the proportion of other species. Conversely, when the interference is harmful, the density of competing species increases. In addition, unlike traditional RPS dynamics, biodiversity can be effectively maintained even in high-mobility regimes. Our study reaffirms the critical role of neutral species in preserving biodiversity.

We investigate the spectral and dynamical properties of the fractional nonlinear Schrödinger equation with harmonic confinement. In this setting, the classical Laplacian is replaced by its fractional power (-∂x2)α/2 with α∈(1,2], introducing nonlocal, Lévy-type dispersion. This modification fundamentally alters the balance between nonlinearity, dispersion, and trapping, reshaping both the structure and stability of stationary states. Using a Fourier pseudo-spectral discretization, we compute stationary branches as functions of the temporal frequency Ω in focusing (σ=+1) and defocusing (σ=-1) regimes, and assess spectral stability via the linearized eigenvalue problem. Direct simulations, performed with split-step and exponential time-differencing integrators, confirm these predictions and reveal α-dependent transitions between coherent oscillations, bounded breathing dynamics, and decoherence or fragmentation. Our results show that decreasing α systematically shifts bifurcation curves, fragments stability windows for excited states, and amplifies instability in the focusing regime, while supporting robust coherence in the defocusing case. Beyond clarifying how harmonic confinement mediates the interplay between nonlinearity and fractional dispersion, the study also provides benchmarks for numerical treatments of fractional operators and points toward potential applications in nonlinear optics, Bose-Einstein condensates, and anomalous transport phenomena.

We study a variant of the one-dimensional swarmalator model where the phase dynamics are pulsatile, governed by a phase-response curve and a pulse function, similar to the Winfree model of regular oscillators. Previously, we studied the idealized case where the individual swarmalators were identical; we generalize this to the more realistic case of non-identical swarmalators, where the natural frequencies are randomly distributed. We find that this heterogeneity leads to new kinds of collective dynamics. These states may be observable in groups of Japanese Tree frogs, circularly confined sperm, or other types of real-world swarmalators.

The computational strategy of recurrent neural networks (RNNs) is encoded in the geometry of their state-space dynamics. We investigate the fundamental differences between two dominant paradigms: fixed-reservoir computing and end-to-end trainable RNNs. On a canonical context-dependent integration task, we systematically compare echo-state networks, gated recurrent units, long short-term memory networks, and simplified linear models. We find that trainable RNNs consistently achieve superior accuracy with significantly fewer parameters. Using methods from dynamical systems and manifold analysis, we uncover the mechanism for this efficiency: trainable networks learn to sculpt their internal dynamics, creating low-dimensional, geometrically organized manifolds that are aligned with the task's computational requirements. In contrast, fixed reservoirs rely on a high-dimensional, entangled representation that is less efficient. These findings, supported by intrinsic dimensionality and spectral analysis, demonstrate that learning to distill task structure into a compact, minimal realization is a hallmark of efficient recurrent computation and connects theoretical principles of universality with biological observations of neural remapping.

Negative information often exerts a disproportionately strong impact on human decision-making, a phenomenon known as the negativity bias. In behavioral economics, this effect is formally captured by prospect theory, which posits that losses loom larger than equivalent gains. For example, a single negative product review can outweigh numerous positive ones, reflecting this principle of loss aversion in consumer behavior. While this psychological effect has been widely documented, its implications for collective opinion dynamics, critical for understanding market stability and reputation dynamics, remain poorly understood. Here, we generalize the q-voter model with independence by introducing opinion-dependent influence group sizes, q+ and q-, which represent the social reinforcement needed to change an opinion from negative to positive and from positive to negative, respectively. We study two versions of this asymmetric model: a baseline model that reduces to the standard q-voter model when q+=q-=q and an extended model that incorporates an additional asymmetry expressed as a preference for one opinion. In its reduced version, this represents a minimal model in terms of non-linearity within the q-voter framework that allows for discontinuous phase transitions and hysteresis. Using mean-field analysis and computer simulations, we show that these modifications lead to rich collective behaviors, including double hysteresis, one form of which is irreversible, providing a mechanism for path-dependence and the sustained, irrecoverable damage to collective sentiment, brand equity, or market confidence.

In prometaphase, microtubules form the spindle structure through dynamic instability, accurately locating and capturing chromosomes to ensure the equal distribution of genetic material (DNA on chromosomes). In this paper, we establish a dynamic model of the microtubule growth-rotation search process by considering the non-local polymerization and depolymerization of microtubules affected by mechanisms such as katanin proteins and kinetochore fibers and derive the macroscopic equation for the microtubule-kinetochore capture model by imposing appropriate boundary conditions. Furthermore, we derive the Feynman-Kac equations that govern the probability density of the functional for the microtubule growth-rotation search model. Finally, we validate the derived equations by comparing results from using a deep learning method to solve the equations with those from applying Monte Carlo simulations to the microscopic models.

Reservoir computing (RC) is a powerful framework for predicting the temporal evolution of variables of nonlinear dynamical systems, yet the role of reservoir topology-particularly symmetry in connectivity and weights-remains not adequately understood. This work investigates how the structure of the reservoir network influences the performance of RC on time series prediction tasks derived from four dynamical systems of increasing complexity: the Mackey-Glass system with delayed-feedback, two nonlinear models of two-dimensional thermal convection flows, and a three-dimensional shear flow model exhibiting transition to turbulence. Using five reservoir topologies in which connectivity patterns and edge weights are controlled independently, we evaluate both direct- and cross-prediction tasks. The results show that symmetric reservoir networks improve prediction accuracy for the convection-based systems when the input dimension is smaller than the number of degrees of freedom. In contrast, the shear-flow model displays almost no sensitivity to topological symmetry due to its strongly chaotic high-dimensional dynamics. These findings reveal how structural properties of reservoir networks affect their ability to learn complex dynamics and provide guidance for designing more effective RC architectures.