| 1. |
- Aidanpää, Jan-Olov, et al.
(författare)
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Stability and bifurcations of a stationary state for an impact oscillator
- 1994
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 4:4, s. 621-630
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Tidskriftsartikel (refereegranskat)abstract
- The motion of a vibroimpacting one-degree-of-freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass-spring-dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe-like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations
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| 2. |
- Bien, Samuel, et al.
(författare)
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Resilience basins of complex systems : An application to prosumer impacts on power grids
- 2023
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Ingår i: Chaos. - 1054-1500 .- 1089-7682. ; 33:6
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Tidskriftsartikel (refereegranskat)abstract
- Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example, the speed of its recovery. We present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a resilience basin, which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving & LE; 70% of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm.
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| 3. |
- Biferale, L., et al.
(författare)
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Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning
- 2019
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500. ; 29:10
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Tidskriftsartikel (refereegranskat)abstract
- To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel that has a slip velocity with fixed intensity, Vs, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasioptimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process and are, therefore, not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when V-s is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small. Published under license by AIP Publishing.
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| 4. |
- Burylko, Oleksandr, et al.
(författare)
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Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
- 2022
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500. ; 32:9
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Tidskriftsartikel (refereegranskat)abstract
- Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked - a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions. Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period-doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos.
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| 5. |
- Calleja, Renato, et al.
(författare)
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Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map
- 2012
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 22:3, s. 033114-
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Tidskriftsartikel (refereegranskat)abstract
- We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical evidence that, close to the breakdown, the angle between the invariant bundles has a linear behavior with respect to the perturbing parameter. This linear behavior agrees with the universal asymptotics of the general framework of breakdown of hyperbolic quasi-periodic tori in skew product systems.
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| 6. |
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| 7. |
- Donges, Jonathan F., et al.
(författare)
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Unified functional network and nonlinear time series analysis for complex systems science : The pyunicorn package
- 2015
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 25:11
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni-and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
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| 8. |
- Donner, Reik V., et al.
(författare)
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Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index
- 2018
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 28:8
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Tidskriftsartikel (refereegranskat)abstract
- Magnetic storms constitute the most remarkable large-scale phenomena of nonlinear magnetospheric dynamics. Studying the dynamical organization of macroscopic variability in terms of geomagnetic activity index data by means of complexity measures provides a promising approach for identifying the underlying processes and associated time scales. Here, we apply a suite of characteristics from recurrence quantification analysis (RQA) and recurrence network analysis (RNA) in order to unveil some key nonlinear features of the hourly Disturbance storm-time (Dst) index during periods with magnetic storms and such of normal variability. Our results demonstrate that recurrence-based measures can serve as excellent tracers for changes in the dynamical complexity along non-stationary records of geomagnetic activity. In particular, trapping time (characterizing the typical length of laminar phases in the observed dynamics) and recurrence network transitivity (associated with the number of the system's effective dynamical degrees of freedom) allow for a very good discrimination between magnetic storm and quiescence phases. In general, some RQA and RNA characteristics distinguish between storm and non-storm times equally well or even better than other previously considered nonlinear characteristics like Hurst exponent or symbolic dynamics based entropy concepts. Our results point to future potentials of recurrence characteristics for unveiling temporal changes in the dynamical complexity of the magnetosphere.
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| 9. |
- Faranda, D., et al.
(författare)
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Dynamical footprints of hurricanes in the tropical dynamics
- 2023
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 33:1
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Tidskriftsartikel (refereegranskat)abstract
- Hurricanes—and more broadly tropical cyclones—are high-impact weather phenomena whose adverse socio-economic and ecosystem impacts affect a considerable part of the global population. Despite our reasonably robust meteorological understanding of tropical cyclones, we still face outstanding challenges for their numerical simulations. Consequently, future changes in the frequency of occurrence and intensity of tropical cyclones are still debated. Here, we diagnose possible reasons for the poor representation of tropical cyclones in numerical models, by considering the cyclones as chaotic dynamical systems. We follow 197 tropical cyclones which occurred between 2010 and 2020 in the North Atlantic using the HURDAT2 and ERA5 data sets. We measure the cyclones instantaneous number of active degrees of freedom (local dimension) and the persistence of their sea-level pressure and potential vorticity fields. During the most intense phases of the cyclones, and specifically when cyclones reach hurricane strength, there is a collapse of degrees of freedom and an increase in persistence. The large dependence of hurricanes dynamical characteristics on intensity suggests the need for adaptive parametrization schemes which take into account the dependence of the cyclone’s phase, in analogy with high-dissipation intermittent events in turbulent flows.
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| 10. |
- Figueras, Jordi-Lluis, et al.
(författare)
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Different scenarios for hyperbolicity breakdown in quasiperiodic area preserving twist maps
- 2015
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 25:12
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Tidskriftsartikel (refereegranskat)abstract
- We present a computer-assisted numerical study of different bifurcations of saddle invariant tori in quasiperiodic area preserving twist maps. We detect three bifurcation scenarios. In the first scenario, the smooth bifurcation, the regularity of the invariant torus is preserved, and the stable and unstable invariant bundles collide smoothly. In the other scenarios, the spiky and folding breakdowns, the invariant torus looses smoothness, and the invariant bundles collide non-smoothly. In the former, the C-1 seminorm of the torus does not blow up while in the latter it does. Numerics suggest that after the breakdowns non-uniformly hyperbolic invariant objects persist. These are qualitatively different depending on the type of breakdown. Finally, using anti-integrable limit theory, we provide a proof of existence of non-uniformly hyperbolic invariant objects for systems very far from the integrable regime.
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