Chaos最新文献

Climate change and anthropogenic impacts have a significant effect on natural ecosystems. As a response, tipping phenomena, i.e., abrupt qualitative changes in the dynamics of ecosystems, like transitions between alternative stable states, can be observed. We study such critical transitions, caused by an interplay between B-tipping, the rate of change of environmental forcing, and a rate-dependent basin boundary crossing. Instead of a slow trend of environmental change, we focus on pulses of variation in the carrying capacity in a simple ecological model, the spruce budworm model, and show how one pulse of environmental change can lead to tracking the current stable state or to tipping to an alternative state depending on the strength and the duration of the pulse. Moreover, we demonstrate that applying a second pulse after the first one, which can track the desired state, can lead to tipping, although its rate is slow and does not even cross the critical threshold. We explain this unexpected behavior in terms of the interacting timescales, the intrinsic ecological timescale, the rate of environmental change, and the movement of the basin boundaries separating the basins of attraction of the two alternative states.

This work presents a heuristic for the selection of a time delay based on optimizing the global maximum of mutual information in orthonormal coordinates for embedding a dynamical system. This criterion is demonstrated to be more robust compared to methods that utilize a local minimum, as the global maximum is guaranteed to exist in the proposed coordinate system for any dynamical system. By contrast, methods using local minima can be ill-posed as a local minimum can be difficult to identify in the presence of noise or may simply not exist. The performance of the global maximum and local minimum methods are compared in the context of causality detection using convergent cross mapping using both a noisy Lorenz system and experimental data from an oscillating plasma source. The proposed heuristic for time lag selection is shown to be more consistent in the presence of noise and closer to an optimal uniform time lag selection.

In this work, effects of constant and time-dependent vaccination rates on the Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) seasonal model are studied. Computing the Lyapunov exponent, we show that typical complex structures, such as shrimps, emerge for given combinations of a constant vaccination rate and another model parameter. In some specific cases, the constant vaccination does not act as a chaotic suppressor and chaotic bands can exist for high levels of vaccination (e.g., >0.95). Moreover, we obtain linear and non-linear relationships between one control parameter and constant vaccination to establish a disease-free solution. We also verify that the total infected number does not change whether the dynamics is chaotic or periodic. The introduction of a time-dependent vaccine is made by the inclusion of a periodic function with a defined amplitude and frequency. For this case, we investigate the effects of different amplitudes and frequencies on chaotic attractors, yielding low, medium, and high seasonality degrees of contacts. Depending on the parameters of the time-dependent vaccination function, chaotic structures can be controlled and become periodic structures. For a given set of parameters, these structures are accessed mostly via crisis and, in some cases, via period-doubling. After that, we investigate how the time-dependent vaccine acts in bi-stable dynamics when chaotic and periodic attractors coexist. We identify that this kind of vaccination acts as a control by destroying almost all the periodic basins. We explain this by the fact that chaotic attractors exhibit more desirable characteristics for epidemics than periodic ones in a bi-stable state.

Complex systems, characterized by intricate interactions among numerous entities, give rise to emergent behaviors whose data-driven modeling and control are of utmost significance, especially when there is abundant observational data but the intervention cost is high. Traditional methods rely on precise dynamical models or require extensive intervention data, often falling short in real-world applications. To bridge this gap, we consider a specific setting of the complex systems control problem: how to control complex systems through a few online interactions on some intervenable nodes when abundant observational data from natural evolution is available. We introduce a two-stage model predictive complex system control framework, comprising an offline pre-training phase that leverages rich observational data to capture spontaneous evolutionary dynamics and an online fine-tuning phase that uses a variant of model predictive control to implement intervention actions. To address the high-dimensional nature of the state-action space in complex systems, we propose a novel approach employing action-extended graph neural networks to model the Markov decision process of complex systems and design a hierarchical action space for learning intervention actions. This approach performs well in three complex system control environments: Boids, Kuramoto, and Susceptible-Infectious-Susceptible (SIS) metapopulation. It offers accelerated convergence, robust generalization, and reduced intervention costs compared to the baseline algorithm. This work provides valuable insights into controlling complex systems with high-dimensional state-action spaces and limited intervention data, presenting promising applications for real-world challenges.

The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, the so-called Koopman eigenvalues and Koopman eigenfunctions, respectively, mirror global properties of the system's flow. In this paper, we perform the Koopman analysis of the singularly perturbed van der Pol system. First, we show the spectral signature depending on singular perturbation: how two Koopman principal eigenvalues are ordered and what distinct shapes emerge in their associated Koopman eigenfunctions. Second, we discuss the singular limit of the Koopman operator, which is derived through the concatenation of Koopman operators for the fast and slow subsystems. From the spectral properties of the Koopman operator for the singularly perturbed system and the singular limit, we suggest that the Koopman eigenfunctions inherit geometric properties of the singularly perturbed system. These results are applicable to general planar singularly perturbed systems with stable limit cycles.

We proposed a neighbor selection mechanism based on memory and target payoff, where the target payoff is the maximum value of the group's average expected payoff. According to this mechanism, individuals prioritize selecting neighbors whose average payoffs in the last M rounds are close to the target payoff for strategy learning, aiming to maximize the group's expected payoff. Simulation results on the grid-based Prisoner's Dilemma and Snowdrift games demonstrate that this mechanism can significantly improve the group's payoff and cooperation level. Furthermore, the longer the memory length, the higher the group's payoff and cooperation level. Overall, the combination of memory and target payoff can lead to the emergence and persistence of cooperation in social dilemmas as individuals are motivated to cooperate based on both their past experiences and future goals. This interplay highlights the significance of taking into account numerous variables in comprehending and promoting cooperation within evolutionary frameworks.

The general form of the Hamiltonian function serves as the foundation for the creation of a new four-dimensional chaotic system in this study. We discover that the external excitation parameter d, the internal parameter a, and all initial values have a transforming influence on the system property. Additionally, the corresponding fractional-order chaotic system in accordance with the constructed four-dimensional chaotic system is proposed. It is found that as the order q rises, the system transforms gradually from a dissipative system to a conservative system. Multiple coexisting attraction flows based on the Hamiltonian energy magnitude are present in this dual-property chaotic system. The complexity analysis shows that the system has a high level of complexity. NIST test indicates that the chaotic sequences produced by this dual-property chaotic system exhibit good pseudo-randomness. Finally, a Digital Signal Processing-based hardware platform confirms the physical realizability of the system.

Human games are inherently diverse, involving more than mere identity interactions. The diversity of game tasks offers a more authentic explanation in the exploration of social dilemmas. Human behavior is also influenced by conformity, and prosociality is a crucial factor in addressing social dilemmas. This study proposes a generalized prisoner's dilemma model of task diversity that incorporates a conformity-driven interaction. Simulation findings indicate that the diversity of multi-tasks and the path dependence contribute to the flourishing of cooperation in games. Conformity-driven interactions also promote cooperation. However, this promotion effect does not increase linearly, and only appropriate task sizes and suitable proportions of conformity-driven interactions yield optimal results. From a broader group perspective, the interplay of network adaptation, task size, and conformity-driven interaction can form a structure of attractors or repellents.

We study the metastability, internal frequencies, activation mechanism, energy transfer, and the collective base-flipping in a mesoscopic DNA via resonance with specific electric fields. Our new mesoscopic DNA model takes into account not only the issues of helicity and the coupling of an electric field with the base dipole moments, but also includes environmental effects, such as fluid viscosity and thermal noise. Also, all the parameter values are chosen to best represent the typical values for the opening and closing dynamics of a DNA. Our study shows that while the mesoscopic DNA is metastable and robust to environmental effects, it is vulnerable to certain frequencies that could be targeted by specific THz fields for triggering its collective base-flipping dynamics and causing large amplitude separation of base pairs. Based on applying the Freidlin-Wentzell method of stochastic averaging and the newly developed theory of resonant enhancement to our mesoscopic DNA model, our semi-analytic estimates show that the required fields should be THz fields with frequencies around 0.28 THz and with amplitudes in the order of 450 kV/cm. These estimates compare well with the experimental data of Titova et al., which have demonstrated that they could affect the function of DNA in human skin tissues by THz pulses with frequencies around 0.5 THz and with a peak electric field at 220 kV/cm. Moreover, our estimates also conform to a number of other experimental results, which appeared in the last couple years.