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Chaos

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https://www.readbyqxmd.com/read/28364776/an-observer-for-an-occluded-reaction-diffusion-system-with-spatially-varying-parameters
#1
Sean Kramer, Erik M Bollt
Spatially dependent parameters of a two-component chaotic reaction-diffusion partial differential equation (PDE) model describing ocean ecology are observed by sampling a single species. We estimate the model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364775/are-continuum-predictions-of-clustering-chaotic
#2
William D Fullmer, Christine M Hrenya
Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ1≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364774/multi-piecewise-quadratic-nonlinearity-memristor-and-its-2n-scroll-and-2n%C3%A2-%C3%A2-1-scroll-chaotic-attractors-system
#3
Chunhua Wang, Xiaoming Liu, Hu Xia
In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364773/diffusion-driven-destabilization-of-spatially-homogeneous-limit-cycles-in-reaction-diffusion-systems
#4
Masataka Kuwamura, Hirofumi Izuhara
We study the diffusion-driven destabilization of a spatially homogeneous limit cycle with large amplitude in a reaction-diffusion system on an interval of finite size under the periodic boundary condition. Numerical bifurcation analysis and simulations show that the spatially homogeneous limit cycle becomes unstable and changes to a stable spatially nonhomogeneous limit cycle for appropriate diffusion coefficients. This is analogous to the diffusion-driven destabilization (Turing instability) of a spatially homogeneous equilibrium...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364772/a-perturbation-theoretic-approach-to-lagrangian-flow-networks
#5
Naoya Fujiwara, Kathrin Kirchen, Jonathan F Donges, Reik V Donner
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364771/smoothing-effect-for-spatially-distributed-renewable-resources-and-its-impact-on-power-grid-robustness
#6
Motoki Nagata, Yoshito Hirata, Naoya Fujiwara, Gouhei Tanaka, Hideyuki Suzuki, Kazuyuki Aihara
In this paper, we show that spatial correlation of renewable energy outputs greatly influences the robustness of the power grids against large fluctuations of the effective power. First, we evaluate the spatial correlation among renewable energy outputs. We find that the spatial correlation of renewable energy outputs depends on the locations, while the influence of the spatial correlation of renewable energy outputs on power grids is not well known. Thus, second, by employing the topology of the power grid in eastern Japan, we analyze the robustness of the power grid with spatial correlation of renewable energy outputs...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364770/on-the-control-of-the-chaotic-attractors-of-the-2-d-navier-stokes-equations
#7
Nejib Smaoui, Mohamed Zribi
The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364769/chaotic-oscillator-containing-memcapacitor-and-meminductor-and-its-dimensionality-reduction-analysis
#8
Fang Yuan, Guangyi Wang, Xiaowei Wang
In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364768/consistency-of-heterogeneous-synchronization-patterns-in-complex-weighted-networks
#9
D Malagarriga, A E P Villa, J Garcia-Ojalvo, A J Pons
Synchronization within the dynamical nodes of a complex network is usually considered homogeneous through all the nodes. Here we show, in contrast, that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364767/the-3-cycle-weighted-spectral-distribution-in-evolving-community-based-networks
#10
Bo Jiao, Xiaoqun Wu
One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Many of these community-based networks evolve over time, that is, we need some size-independent metrics to capture the connection relationships embedded in these clusters. One of these metrics is the average clustering coefficient, which represents the triangle relationships between all nodes of networks. However, the vast majority of network communities is composed of low-degree nodes...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364766/chaos-emerging-in-soil-failure-patterns-observed-during-tillage-normalized-deterministic-nonlinear-prediction-ndnp-and-its-application
#11
Kenshi Sakai, Shrinivasa K Upadhyaya, Pedro Andrade-Sanchez, Nina V Sviridova
Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364765/modeling-the-network-dynamics-of-pulse-coupled-neurons
#12
Sarthak Chandra, David Hathcock, Kimberly Crain, Thomas M Antonsen, Michelle Girvan, Edward Ott
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364764/design-and-implementation-of-dynamic-logic-gates-and-r-s-flip-flop-using-quasiperiodically-driven-murali-lakshmanan-chua-circuit
#13
P R Venkatesh, A Venkatesan, M Lakshmanan
We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as "region of signal propagation." Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the "region of logical operation...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364763/understanding-the-geometry-of-transport-diffusion-maps-for-lagrangian-trajectory-data-unravel-coherent-sets
#14
Ralf Banisch, Péter Koltai
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a method for extracting coherent sets from possibly sparse Lagrangian trajectory data. Our method can be seen as an extension of diffusion maps to trajectory space, and it allows us to construct "dynamical coordinates," which reveal the intrinsic low-dimensional organization of the data with respect to transport...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364762/levitation-of-heavy-particles-against-gravity-in-asymptotically-downward-flows
#15
Jean-Régis Angilella, Daniel J Case, Adilson E Motter
In the fluid transport of particles, it is generally expected that heavy particles carried by a laminar fluid flow moving downward will also move downward. We establish a theory to show, however, that particles can be dynamically levitated and lifted by interacting vortices in such flows, thereby moving against gravity and the asymptotic direction of the flow, even when they are orders of magnitude denser than the fluid. The particle levitation is rigorously demonstrated for potential flows and supported by simulations for viscous flows...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364761/stochasticity-induced-mixed-mode-oscillations-and-distribution-of-recurrent-outbreaks-in-an-ecosystem
#16
Susmita Sadhu
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We explore the effect of stochasticity in the excitable regime, leading to dynamics that are not anticipated by its deterministic counterpart. The stochastic model admits several kinds of noise-driven mixed-mode oscillations which capture the intermediate dynamics between two cycles of population outbreaks...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364760/chimera-states-and-the-interplay-between-initial-conditions-and-non-local-coupling
#17
Peter Kalle, Jakub Sawicki, Anna Zakharova, Eckehard Schöll
Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are linked to the occurrence of chimera states, flipped profiles of the mean phase velocity, and the transition from a phase- to an amplitude-mediated chimera state...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364759/clustering-coefficient-and-periodic-orbits-in-flow-networks
#18
Victor Rodríguez-Méndez, Enrico Ser-Giacomi, Emilio Hernández-García
We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e., graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations, the clustering coefficient still identifies cyclic motion between regions of the fluid...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364758/predictability-of-large-scale-atmospheric-motions-lyapunov-exponents-and-error-dynamics
#19
Stéphane Vannitsem
The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos, this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is shown in particular that the variability of the local Lyapunov exponents (corresponding to the dominant Lyapunov exponent) decreases when the model resolution increases...
March 2017: Chaos
https://www.readbyqxmd.com/read/28364757/regenerating-time-series-from-ordinal-networks
#20
Michael McCullough, Konstantinos Sakellariou, Thomas Stemler, Michael Small
Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches...
March 2017: Chaos
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