Chaos最新文献

In this article, we explore the possibility of a sub-harmonic (1:2) entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a fast external forcing, through the variation of the amplitude of the external fast signal. We also deduce the condition for the threshold parametric strength required to generate sub-harmonic oscillation. The Blekhman perturbation (direct partition of motion) and the Renormalization group technique have been employed to study how the signal amplitude plays a pivotal role in modulating the limit-cycle dynamics as well as the subharmonic generation. While the conventional studies use forcing strength as the control parameter, we use the signal strength as the tuning element, appearing as a more efficient and physically observable measure. Our analytical estimations are well supported by numerical simulations.

Delayed feedback control is a common technique for the stabilization of unstable periodic orbits in chaotic systems. Most results in this area rely on linear control techniques, which do not have guaranteed performance for nonlinear systems. Whereas nonlinear control methods have already been proposed, the existing results often rely on knowledge or partial knowledge of the system parameters and also have no mechanism for reaching the possible natural responses of the underlying uncontrolled system with embedded unstable periodic orbits. The main contribution of this paper is to propose a control method for a class of chaotic systems with entirely unknown parameters. Based on the delayed information of the system states, we develop an adaptive control strategy such that the system states converge to a periodic response with a desired time period. While infinitely many periodic responses are possible, the proposed control strategy is equipped with a mechanism that steers the dynamics toward the possible natural periodic responses of the system, such as unstable periodic orbits, where the controller is noninvasive. The proposed control strategy is demonstrated through simulation and used for revealing unstable periodic orbits inside the chaotic attractor of a Duffing oscillator.

Bifurcation analysis is applied to the FitzHugh-Nagumo oscillator driven by a sinusoidal source. A numerically generated 2D regime map showing a variety of oscillatory dynamics in the parameter space of source frequency and amplitude agrees well with a map created from analog circuit measurements. Application of the sinusoidal source to the fast variable's first-order differential equation produces an island in the map in which oscillations at the source frequency are unstable and the behavior is dominated by two distinct families of subharmonic limit cycles and by chaos. Previously published maps are portions of the map shown here and are shown to be consistent with it. The more detailed and comprehensive regime map presented here should facilitate the understanding of this foundational system, thereby aiding the ongoing research involving more complicated implementations of the FitzHugh-Nagumo system.

We study a class of stochastic resetting (SR) processes in which a diffusing particle alternates between free motion and confinement by an externally controlled potential. When the particle is recaptured, it undergoes a return trajectory that drives it toward a designated reset point. In standard SR, such returns are treated as instantaneous, but in realistic setups, they have finite duration and introduce imprecision in the starting points of subsequent search attempts. We analyze a fluctuating harmonic potential in which return trajectories are forcibly terminated the moment the particle reaches the origin, ensuring that all outward (diffusive) trajectories begin from the same point. This is implemented through instantaneous positional information: a feedback signal that shortens the return phase without incurring additional energetic cost. We examine several search protocols built on this mechanism and determine their mean first-passage times (MFPTs). Of particular interest is a protocol in which outward diffusion is eliminated entirely and the return motion itself becomes the search mechanism. This "search by return" perspective reverses the conventional logic of SR and yields a closed-form MFPT.

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.