Chaos最新文献

In this paper, the complex and dynamically rich distribution of stable phases in the well-known discrete Ikeda map is studied in detail. The unfolding patterns of these stable phases are described through three complementary stability diagrams: the Lyapunov stability diagram, the isoperiod stability diagram, and the isospike stability diagram. The adding-doubling complexification cascade and fascinating non-quantum chiral pairs are discovered, marking the first report of such structures in discrete mapping. The inherent symmetry of the Ikeda map also leads to the emergence of even more complex chiral formations. Additionally, the effects of initial value perturbations on stable phase topology are explored, revealing that in near-conservative states, small changes in initial conditions significantly disturb the system, resulting in the discovery of a multitude of previously hidden shrimp islands. Our findings enhance the understanding of non-quantum chiral structures within discrete systems and offer new insights into the intricate manifestations of stability and multistability in complex mappings.

We propose a method based on autoencoders to reconstruct attractors from recorded footage, preserving the topology of the underlying phase space. We provide theoretical support and test the method with (i) footage of the temperature and stream function fields involved in the Lorenz atmospheric convection problem and (ii) a time series obtained by integrating the Rössler equations.

We propose a novel approach to investigate the brain mechanisms that support coordination of behavior between individuals. Brain states in single individuals defined by the patterns of functional connectivity between brain regions are used to create joint symbolic representations of brain states in two or more individuals to investigate symbolic dynamics that are related to interactive behaviors. We apply this approach to electroencephalographic data from pairs of subjects engaged in two different modes of finger-tapping coordination tasks (synchronization and syncopation) under different interaction conditions (uncoupled, leader-follower, and mutual) to explore the neural mechanisms of multi-person motor coordination. Our results reveal that dyads exhibit mostly the same joint symbols in different interaction conditions-the most important differences are reflected in the symbolic dynamics. Recurrence analysis shows that interaction influences the dwell time in specific joint symbols and the structure of joint symbol sequences (motif length). In synchronization, increasing feedback promotes stability with longer dwell times and motif length. In syncopation, leader-follower interactions enhance stability (increase dwell time and motif length), but mutual interaction dramatically reduces stability. Network analysis reveals distinct topological changes with task and feedback. In synchronization, stronger coupling stabilizes a few states, preserving a core-periphery structure of the joint brain states while in syncopation we observe a more distributed flow amongst a larger set of joint brain states. This study introduces symbolic representations of metastable joint brain states and associated analytic tools that have the potential to expand our understanding of brain dynamics in human interaction and coordination.

We investigate the aging transition in networks of excitable and self-oscillatory units as the fraction of inherently excitable units increases. Two network topologies are considered: a scale-free network with weighted pairwise interactions and a two-dimensional simplicial complex with weighted scale-free pairwise and triadic interactions. Without triadic interactions, the aging transition from collective oscillations to oscillation death (inhomogeneous stationary states) can occur either suddenly or through an intermediate state of partial oscillation. However, when triadic interactions are present, the network becomes less resilient, and the transition occurs without partial oscillation at any coupling strength. Furthermore, we observe the presence of inhomogeneous steady states within the complete oscillation death regime, regardless of the network interaction models.

The aircraft can experience complex environments during the flight. For the random actions, the traditional Gaussian white noise assumption may not be sufficient to depict the realistic stochastic loads on the wing structures. Considering fluctuations with extreme conditions, Lévy noise is a better candidate describing the stochastic dynamical behaviors on the airfoil models. In this paper, we investigated a classical two-dimensional airfoil model with the nonlinear pitching stiffness subjected to the Lévy noise. For the deterministic case, the nonlinear stiffness coefficients reshape the bistable region, which influences the size of the large limit cycle oscillations before the flutter speed. The introduction of the additive Lévy noise can induce significant inverse stochastic resonance phenomena when the basin of attraction of the stable limit cycle is much smaller than that of the stable fixed point. The distribution parameters of the Lévy noise exhibit distinct impacts on the inverse stochastic resonance curves. Our results may shed some light on the design and control process of the airfoil models.

The existing research studies on the basin stability of stochastic systems typically focus on smooth systems, or the attraction basins are pre-defined as easily solvable regular basins. In this work, we introduce a new framework to discover the basin stability from state time series in the non-smooth stochastic competition system under threshold control. Specifically, we approximate the drift and diffusion with threshold control parameters by an extended Kramers-Moyal expansion with initial state partitioning. Then, we calculate the first transition probability of irregular attraction basins by applying a difference scheme and smooth approximation methods for the system. Numerical simulations of the original system validate the accuracy of the identified drift and diffusion terms, as well as the smooth approximation. Our findings reveal that threshold control modifies the influence of environmental noise on the system basin stability.

Spirals are a special class of excitable waves that have its significance in the understanding of cardiac arrests and neuronal transduction. In a theoretical model of the chemical Belousov-Zhabotinsky reaction system, we explore the dynamics of the spatiotemporal patterns that emerge out of competing reaction and diffusion phenomena. By modifying the existing mathematical models of the reaction kinetics, we have been able to explore the explicit effect of hydrogen ion concentration in the system, so as to achieve various regimes of wave activity, from stable spirals to oscillation death. In between the two extremes, we show how instability sets in, with anisotropy leading to drifting spirals, core defects resulting in spiral breakup and turbulence, chaotic oscillations, and target patterns, before the system finally reaches a non-oscillating steady state. On varying other stoichiometric parameters, we also illustrate the changes in system dynamics and wave properties.

Generosity through donation plays a crucial role in reducing inequality and influencing human behavior. However, previous research on donation has overlooked individuals' acceptance of the extent of inequality, which acts as a trigger for donation. To address this gap, this paper systematically explores the impact of donation based on inequality tolerance on the evolution of cooperation in spatial public goods game. Specifically, donation occurs only when an individual's payoff advantage exceeds her inequality tolerance. The results show that donation patterns are crucial for the emergence and stability of cooperation. In the enduring period, the defector-to-cooperator donation pattern helps to form cooperative clusters. In the expanding period, cooperator-to-cooperator, defector-to-defector, and defector-to-cooperator donation patterns create a stable three-layer structure through self-organization, providing a payoff advantage to boundary cooperators. As donation ratio increases, the three-layer structure provides a greater payoff advantage to boundary cooperators, leading to an increase in cooperation. As inequality tolerance increases, changes in donation patterns weaken the three-layer structure, causing cooperation to decrease or disappear through discontinuous phase transitions. Subsequently, all critical points of discontinuous phase transitions are identified by specific spatial configurations. In addition, the influence of donation patterns on the evolution of cooperation is robust, even in heterogeneous small-world networks. This paper offers valuable insights into the dynamics of cooperation evolution and the role of donation in shaping behavior.

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper, we aim to address a gap in the literature, namely, to examine how the gradual improvement of power grid models affects the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying levels of heterogeneity through the coupling strength, the nodal powers, and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency, and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. Even the most heterogeneous models showed notable synchronization, encouraging the use of such models. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior.

Detecting directional couplings from time series is crucial in understanding complex dynamical systems. Various approaches based on reconstructed state-spaces have been developed for this purpose, including a cross-distance vector measure, which we introduced in our recent work. Here, we devise two new cross-vector measures that utilize ranks and time series estimates instead of distances. We analyze various deterministic and stochastic dynamics to compare our cross-vector approach against some established state-space-based approaches. We demonstrate that all three cross-vector measures can identify the correct coupling direction for a broader range of couplings for all considered dynamics. Among the three cross-vector measures, the rank-based variant performs the best. Comparing this novel measure to an established rank-based measure confirms that it is more noise-robust and less affected by linear cross-correlation. To extend this comparison to real-world signals, we combine both measures with the method of surrogates and analyze a database of electroencephalographic (EEG) recordings from epilepsy patients. This database contains signals from brain areas where the patients' seizures were detected first and signals from brain areas that were not involved in the seizure onset. A better discrimination between these signal classes is obtained by the cross-rank vector measure. Additionally, this measure proves to be robust to non-stationarity, as its results remain nearly unchanged when the analysis is repeated for the subset of EEG signals that were identified as stationary in previous work. These findings suggest that the cross-vector approach can serve as a valuable tool for researchers analyzing complex time series and for clinical applications.