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Matthias F Wolff, Pedro G Lind, Philipp Maass
Power flow dynamics in electricity grids can be described by equations resembling a Kuramoto model of non-linearly coupled oscillators with inertia. The coupling of the oscillators or nodes in a power grid generally exhibits pronounced heterogeneities due to varying features of transmission lines, generators, and loads. In studies aiming at uncovering mechanisms related to failures or malfunction of power systems, these grid heterogeneities are often neglected. However, over-simplification can lead to different results away from reality...
October 2018: Chaos
Liyuan Zhang, Denggui Fan, Qingyun Wang, Gerold Baier
Brain-derived neurotrophic factor (BDNF) has recently been implicated in the modulation of receptor activation leading to dynamic state transitions in temporal lobe epilepsy (TLE). In addition, the crucial role of neuronal noise in these transitions has been studied in electrophysiological experiments. However, the precise role of these factors during seizure generation in TLE is not known. Building on a previously proposed model of an epileptogenic hippocampal network, we included the actions of BDNF-regulated receptors and intrinsic noise...
October 2018: Chaos
Yongshuai Zhang, Deqin Qiu, Dumitru Mihalache, Jingsong He
The first-order rogue wave solution with two arbitrary parameters of the Wadati-Konno-Ichikawa equation is generated based on the Darboux transformation and inverse hodograph transformation. The analyticity of first-order rogue wave solution is studied. A simple analysis shows that the parameter that denotes the amplitude of background wave plays an important role in controlling the analyticity of rogue wave solution. In particular, the rogue wave solution displays a loop-type profile when it is singular, and the general features of loop rogue waves are discussed in detail...
October 2018: Chaos
J Noetel, V L S Freitas, E E N Macau, L Schimansky-Geier
We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home. The model describes the kinematic motion of the object with constant speed in two dimensions. The angular dynamics is driven by noise and describes a "pursuit" and "escape" behavior of the heading and the position vectors. Pursuit behavior ensures the return to the home and the escaping between the two vectors realizes exploration of space in the vicinity of the given home...
October 2018: Chaos
Giuseppe D'Onofrio, Massimiliano Tamborrino, Petr Lansky
The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically...
October 2018: Chaos
Hyunsuk Hong
We consider a system of coupled swarmalators moving in two dimensional space and explore its collective behavior. Here the swarmalators represent the oscillators that can sync and swarm in space, following the previous study [O'Keeffe et al. , Nat. Commun., 8 , 1504 (2017)]. The internal state of each swarmalator is represented by its phase angle, and the swarmalators are free to move in the plane according to an equation of motion where the phase and spatial dynamics are coupled with each other. In particular, the phase coupling between the swarmalators is attractive (positive) one, so the coupling makes the swarmalators have their phase difference minimized...
October 2018: Chaos
Evgeny Grines, Grigory Osipov, Arkady Pikovsky
Phase response curve is an important tool in the studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a perturbation, transitions from one oscillating mode to another one may occur. We define phase transfer curves to describe the phase shifts at such transitions. This allows for a construction of one-dimensional maps that characterize periodically kicked multistable oscillators...
October 2018: Chaos
Rosangela Follmann, Annabelle Shaffer, Zachary Mobille, George Rutherford, Epaminondas Rosa
We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition...
October 2018: Chaos
Lubomir Kostal, Petr Lansky, Michael Stiber
The rate coding hypothesis is the oldest and still one of the most accepted and investigated scenarios in neuronal activity analyses. However, the actual neuronal firing rate, while informally understood, can be mathematically defined in several different ways. These definitions yield distinct results; even their average values may differ dramatically for the simplest neuronal models. Such an inconsistency, together with the importance of "firing rate," motivates us to revisit the classical concept of the instantaneous firing rate...
October 2018: Chaos
Philine Granitza, Jan F Kraemer, Christoph Schoebel, Thomas Penzel, Jürgen Kurths, Niels Wessel
Cheyne-Stokes respiration (CSR) is a periodic, highly dynamic, respiratory pattern and a known comorbidity in congestive heart failure (CHF) patients. It is generally seen as an indicator for a negative prognosis, even if no distinction in degree is known or understood. This paper aims to improve on existing attempts by creating a quantification of the behavior of the dynamic desaturation process of oxygen in the blood. We performed this work on a cohort of <mml:math xmlns:mml=""> <mml:mn>11</mml:mn> </mml:math> subjects with CHF, reduced left ventricular ejection fraction, and CSR...
October 2018: Chaos
A R Brazhe, D E Postnov, O Sosnovtseva
Inspired by calcium activity in astrocytes, which is different in the cell body and thick branches on the one hand and thin branchlets and leaflets on the other hand, we formulate a concept of spatially partitioned oscillators. These are inhomogeneous media with regions having different excitability properties, with a global dynamics governed by spatial configuration of such regions. Due to a high surface-to-volume ratio, calcium dynamics in astrocytic leaflets is dominated by transmembrane currents, while somatic calcium dynamics relies on exchange with intracellular stores, mediated by IP <mml:math xmlns:mml="http://www...
October 2018: Chaos
B M Barlow, B Joos, A K Trinh, A Longtin
Mild traumatic injury can modify the key sodium (Na+ ) current underlying the excitability of neurons. It causes the activation and inactivation properties of this current to become shifted to more negative trans-membrane voltages. This so-called coupled left shift (CLS) leads to a chronic influx of Na+ into the cell that eventually causes spontaneous or "ectopic" firing along the axon, even in the absence of stimuli. The bifurcations underlying this enhanced excitability have been worked out in full ionic models of this effect...
October 2018: Chaos
Vera Bettenworth, Matthew McIntosh, Anke Becker, Bruno Eckhardt
Many bacterial species exchange signaling molecules to coordinate population-wide responses. For this process, known as quorum sensing, the concentration of the respective molecules is crucial. Here, we consider the interaction between spatially distributed bacterial colonies so that the spreading of the signaling molecules in space becomes important. The exponential growth of the signal-producing populations and the corresponding increase in signaling molecule production result in an exponential concentration profile that spreads with uniform speed...
October 2018: Chaos
Hans Liljenström
One of the greatest challenges to science, in particular, to neuroscience, is to understand how processes at different levels of organization are related to each other. In connection with this problem is the question of the functional significance of fluctuations, noise, and chaos. This paper deals with three related issues: (1) how processes at different organizational levels of neural systems might be related, (2) the functional significance of non-linear neurodynamics, including oscillations, chaos, and noise, and (3) how computational models can serve as useful tools in elucidating these types of issues...
October 2018: Chaos
Ayan Biswas, Suman K Banik
The formalism of partial information decomposition provides a number of independent components which altogether constitute the total information provided by the source variable(s) about the target variable(s). These non-overlapping terms are recognized as unique information, synergistic information, and redundant information. The metric of net synergy conceived as the difference between synergistic and redundant information is capable of detecting effective synergy, effective redundancy, and information independence among stochastic variables...
October 2018: Chaos
Qingchu Wu, Gaoxi Xiao
We study the impact of susceptible nodes' awareness on epidemic spreading in social systems, where the systems are modeled as multiplex networks coupled with an information layer and a contact layer. We develop a colored heterogeneous mean-field model taking into account the portion of the overlapping neighbors in the two layers. With theoretical analysis and numerical simulations, we derive the epidemic threshold which determines whether the epidemic can prevail in the population and find that the impacts of awareness on threshold value only depend on epidemic information being available in network nodes' overlapping neighborhood...
October 2018: Chaos
Felix Tretter
Psychiatric illnesses like dementia are increasingly relevant for public health affairs. Neurobiology promises progress in diagnosis and treatment of these illnesses and exhibits a rapid increase of knowledge by new neurotechnologies. In order to find generic patterns in huge neurobiological data sets and by exploring formal brain models, non-linear science offers many examples of fruitful insights into the complex dynamics of neuronal information processing. However, it should be minded that neurobiology neither can bridge the explanatory gap between brain and mind nor can substitute psychological and psychiatric categories and knowledge...
October 2018: Chaos
Vidit Agrawal, Andrew B Cowley, Qusay Alfaori, Daniel B Larremore, Juan G Restrepo, Woodrow L Shew
It is widely appreciated that balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, balance could be achieved by many possible configurations of excitatory and inhibitory synaptic strengths and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses or a few inhibitory neurons with strong synapses. Among the continuum of different but balanced configurations, why should any particular configuration be favored? Here, we address this question in the context of the entropy of network dynamics by studying an analytically tractable network of binary neurons...
October 2018: Chaos
Volker Mehrmann, Riccardo Morandin, Simona Olmi, Eckehard Schöll
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model with inertia. The usual formulation in the form of a system of coupled ordinary differential equations is not always adequate...
October 2018: Chaos
Linjie Liu, Shengxian Wang, Xiaojie Chen, Matjaž Perc
Pro-social punishment and exclusion are common means to elevate the level of cooperation among unrelated individuals. Indeed, it is worth pointing out that the combined use of these two strategies is quite common across human societies. However, it is still not known how a combined strategy where punishment and exclusion are switched can promote cooperation from the theoretical perspective. In this paper, we thus propose two different switching strategies, namely, peer switching that is based on peer punishment and peer exclusion, and pool switching that is based on pool punishment and pool exclusion...
October 2018: Chaos
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