Chaos最新文献

The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing, assessing, and controlling oscillation quenching using coupling functions. Specifically, by observing limit-cycle oscillators, we investigate the bifurcations and dynamical transitions induced by time-varying diffusive and periodic coupling functions. We studied the transitions between oscillation quenching states induced by the time-varying form of the coupling function while the coupling strength is kept invariant. The time-varying periodic coupling function allowed us to identify novel, non-trivial inhomogeneous states that have not been reported previously. Furthermore, by using dynamical Bayesian inference, we have also developed a Proportional Integral controller that maintains the oscillations and prevents oscillation quenching from occurring. In addition to the present implementation and its generalizations, the framework carries broader implications for identification and control of oscillation quenching in a wide range of systems subjected to time-varying interactions.

The conversion of nicotinamide adenine dinucleotide (NAD+) to its reduced form (NADH) by dehydrogenases is a key step in numerous redox reactions and, consequently, in cellular energy conversion. NADH autofluorescence imaging represents a promising method for the optical detection of metabolic dysfunction in living tissues. However, it is sensitive to the total NAD(H) content as well as to variations in absorption and light scattering, which may fluctuate independently. A major objective is, therefore, to identify invariant quantities that are responsive to reversible ischemic tissue injury while circumventing the limitations of intensity-based imaging. We show experimentally and in silico that glutamate dehydrogenase (GDH) drives the NAD+/NADH balance toward a competing semi-equilibrium (CSE) state when an external catalytic process promotes the NADH → NAD+ conversion. This CSE state is uniquely determined by the total NAD(H) pool, the GDH concentration, and the external catalytic activity. Experimental validation using UV-induced NADH photolysis (300-500 mW/cm2), implementing the NADH → NAD+ reaction, showed that GDH activity can be estimated in the epicardium of ex vivo Langendorff-perfused hearts by analyzing the CSE. These results present a new approach to the optical assessment of tissue metabolic activity based on autofluorescence imaging of NADH. Our method allows the assessment of cardiac tissue ischemia without knowledge of the photolysis rate, thereby overcoming the inherent limitations of optical detection in living tissues.

Reservoir computing has attracted considerable attention as an effective method for learning chaotic time series generated by dynamical systems. In this paper, we propose a new reservoir computing approach that is adapted to dynamical systems on general manifolds, representing a natural extension of the usual method for dynamical systems on the Euclidean spaces. We also present numerical results for learning the hyperbolic toral automorphism and the tripling map on the circle to demonstrate that the proposed method performs effectively.

We investigate the long-term dynamics of a nonautonomous Bonifacio-Lugiato model of optical superfluorescence. The scalar ordinary differential equation modeling the phenomenon is given by a concave-convex autonomous function of the state variable that is excited by a time-dependent input, Λ(t). We describe the system's response in terms of the dynamical characteristics of the input function, with particular focus on the cases of uniform stability-when exactly a bounded solution exists, which in addition is hyperbolic attractive-or bistability-when two stable solutions of this type coexist. Our starting point is the open interval delimited by the constant input values λ for which the autonomous version of our model was already known to exhibit bistability: we prove that, in general, bistability occurs when Λ(t) lies within this interval. This condition is sufficient but not necessary. Applying nonautonomous bifurcation methods and imposing more restrictive conditions on the variation of Λ(t), we can determine the necessary and sufficient conditions for bistability and to prove that the general response is uniform stability when these conditions are not satisfied. Finally, we analyze the case of a periodic input that varies on a slow timescale using fast-slow system methods to rigorously establish either a uniformly stable or a bistable response.

In this paper, we revisit the classical perturbed Duffing system and investigate its intricate dynamical behavior through the numerical method based on the topological horseshoe theory employing the Runge-Kutta method. Based on the classical Melnikov analysis, we explore the persistence of chaotic dynamics beyond the parameter regimes in which the Melnikov condition guarantees the existence of a transverse homoclinic intersection. Specifically, we examine the second return map and demonstrate the existence of a topological horseshoe at parameter values εγ=0.4, εδ=0.54, and ω=1. This provides numerical evidence to Smale horseshoe-type chaos in a regime where the Melnikov criterion is not satisfied. Furthermore, we provide a more rigorous treatment on the existence of the topological horseshoe in terms of crossing stability.

Evolutionary game-based models hold a potential key to help interpret the evolution of systems based on the interaction of multispecies. In particular, in ecosystems with structures such as food webs, the extinction of one species through competition can lead to secondary extinctions, and such ecological cascades are common in cyclic game systems governed by the rock-paper-scissors metaphor. In this paper, we delve into ecological cascades in the evolution of cyclically competing populations by using directed graphs. By revisiting previous studies of cyclic game systems, we identify a common mathematical property in evolutionary directed graphs and predict evolution in terms of tournaments. We further compare a theoretical result with Monte Carlo simulations, which shows that the graph-based interpretation of ecological cascades is qualitatively consistent with numerical simulations. Ultimately, we may emphasize that the method based on directed graphs would be more practical for understanding the evolution of multispecies than numerical simulations.

Inspired by the physical property of charge-controlled memristor, equivalent memristive current and charge variable are used to describe the wave stability in cardiac tissue under an electric field. The memristive current generated in a single myocardial cell results from the changes in the static distribution of intracellular ions and external forced electric field. A reaction-diffusion equation is used to estimate the propagation of electrical signals in the cardiac tissue as traveling waves, and the variations in memristive currents and charge levels reflect the effect of the electric field on the cardiac electrical behaviors, which are illustrated by the wave propagation and patterns' stability in the excitable media. An external stimulus is applied to control the wave propagation, and the self-sustained wave property is explored. An external electric field is applied to control the charge pumping and the wave stability is controlled. The improved memristive cardiac model considering the effect of electric fields is converted into an equivalent neural network for finding a numerical solution, and the statistical synchronization factor and energy function are defined for the theoretical analysis. This theoretical memristive cardiac model is effective to discover the wave characteristic, and then, an appropriate control scheme can be applied to prevent wave instability (breakup of spiral waves). As a result, heartbeat is maintained by generating and propagating continuous wavefronts in the cardiac tissue, and then, blood is pumped in and out of the heart exposed to an external electric field.

Mpox (monkeypox) is a re-emerging viral disease with increasingly sustained human transmission, particularly in previously unaffected regions. In this study, we develop a compartmental epidemic model that captures mpox transmission dynamics and incorporates a treatment function to assess the impact of medical interventions on disease progression and recovery. The model is calibrated using U.S. case data, with parameters estimated via the Trust Region Reflective optimization method to ensure close alignment with observed trends. We perform global sensitivity analysis using partial rank correlation coefficients to identify key parameters influencing transmission. The model's bifurcation structure is examined through the basic reproduction number RM0, revealing both forward and backward bifurcations that highlight threshold behavior and the potential for complex endemic dynamics. For real-time forecasting, we incorporate prior knowledge of mpox dynamics into machine learning models, ARNN (Autoregressive Neural Network), ARIMA (Autoregressive Integrated Moving Average), and LSTM (Long Short-Term Memory), achieving improved predictive accuracy over traditional methods. These epidemic-informed models benefit from mechanistic insights, enhancing their responsiveness to changing trends. Our results emphasize the importance of timely treatment, hygiene, and vaccination in mitigating mpox spread. The integrated modeling and the forecasting framework provide valuable tools for anticipating outbreaks and informing public health strategies.

In this paper, we study the influence of high-order interactions and coupling adaptivity on the dynamics of coupled oscillators. We found that the introduction of second-order adaptive couplings leads to the emergence of a new type of synchronous behavior in the form of double antipodal clusters, which was not observed in the case of pairwise interactions. We also discovered various scenarios for the emergence of hierarchical synchronization patterns, including multicluster and chimera states. In this case, the process of sequential formation of synchronous groups includes two stages with characteristic properties. The first stage is associated with the emergence in part of the network of a pair of high-frequency and low-frequency synchronous groups, the sizes of which are ordered in a hierarchical way. The emergence of such pairs is accompanied by the suppression of the impact from the rest of the network oscillators and the presence of strong interaction within each pair. During the second stage, the process of synchronization of the remaining incoherent part of the network occurs. Due to high-order interactions, this process is determined by the presence of a complex structure of interactions in the network, which can lead to the emergence of transient synchronous sets.

Delay-feedback reservoirs are a subset of reservoir computers characterized by a hardware-efficient architecture that trades spatial complexity for temporal processing. It employs a single non-linear node, a delay line, and a time-multiplexed input signal to generate a network of "virtual nodes," effectively emulating a larger spatial neural network. One of the most powerful aspects of delay-feedback reservoirs is their versatility. Our previous work found that the non-linear node performs two mathematical functions, a non-linear transform and integration. The non-linear transform can be represented by any number of non-linear functions, making it difficult to optimize a delay-feedback reservoir to solve a specific computational task. This work explores different non-linear functions in order to determine their effect on the dynamics of the reservoir, in order to provide insight into this optimization problem. Five different non-linear functions are compared in terms of performance, metrics, and utilization: Mackey-Glass, sine squared, double sinusoids, Tan, and Tanh. Our results find that the Mackey-Glass non-linear function shows limited system dynamics, performing well on non-linear tasks but performing poorly on memory intensive tasks. We then demonstrate the distinct system dynamics within the other four non-linear functions. We found that sine squared shows limited overall performance, double sinusoid performs well in non-linear tasks, Tan resembles an odd valued exponent Mackey-Glass reservoir but with greater parameter sensitivity, and tanh offers balanced performance across both task types. We find that modifying the system dynamics of a reservoir is an important step toward optimizing a delay-feedback reservoir for specific computational tasks.