scholarly journals Dynamics of Structured Networks of Winfree Oscillators

2021 ◽  
Vol 15 ◽  
Author(s):  
Carlo R. Laing ◽  
Christian Bläsche ◽  
Shawn Means
Keyword(s):  
Differential Equations ◽  
Structural Property ◽  
Heterogeneous Networks ◽  
Network Structure ◽  
Response Curve ◽  
Phase Response Curve ◽  
Phase Oscillator ◽  
Interaction Function ◽  
Different Types ◽  
Low Dimensional

Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.

Modulation of Hydra attenuata rhythmic activity: phase response curve

1976 ◽  
Vol 65 (3) ◽  
pp. 737-751
Author(s):  
C. Taddei-Ferretti ◽  
L. Cordella
Keyword(s):  
Response Curve ◽  
Phase Response Curve ◽  
Rhythmic Activity ◽  
Light Stimulation ◽  
Pulse Trains ◽  
Activity Phase ◽  
Photic Stimulus ◽  
Different Types ◽  
Hydra Attenuata ◽  
Stimulation Of

We investigated the effect of photic stimulation on the frequency of Hydra attenuata column contractions. We used positive or negative abrupt light transitions, single or repetitive light or darkness pulses, and alternation of light and darkness periods. The main results are: (a) The frequency of the contraction pulse trains (CPTs) varies transiently in response to an abrupt variation of the light intensity. (b) CPTs in progress can be inhibited by different types of photic stimuli. (c) The response time to a single photic stimulus varies during the inter-CPT interval and depends also on the polarity of the stimulus. (d) The CPTs are entrainable with repetitive light stimulation of various frequencies. (e) Long-lasting variations of the frequency of CPTs occur after the end of a repetitive light stimulation. We suggest that the mechanism responsible for the rhythym of column contractions is quite similar to that on which other biological rhythmic phenomena are based.

scholarly journals Dynamics in the Sakaguchi-Kuramoto model with bimodal frequency distribution

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243196
Author(s):  
Shuangjian Guo ◽  
Yuan Xie ◽  
Qionglin Dai ◽  
Haihong Li ◽  
Junzhong Yang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Natural Frequency ◽  
Frequency Distribution ◽  
Bimodal Distribution ◽  
Kuramoto Model ◽  
Phase Lag ◽  
Phase Oscillators ◽  
Different Types ◽  
Low Dimensional

In this work, we study the Sakaguchi-Kuramoto model with natural frequency following a bimodal distribution. By using Ott-Antonsen ansatz, we reduce the globally coupled phase oscillators to low dimensional coupled ordinary differential equations. For symmetrical bimodal frequency distribution, we analyze the stabilities of the incoherent state and different partial synchronous states. Different types of bifurcations are identified and the effect of the phase lag on the dynamics is investigated. For asymmetrical bimodal frequency distribution, we observe the revival of the incoherent state, and then the conditions for the revival are specified.

scholarly journals Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1168
Author(s):  
Cheon Seoung Ryoo ◽  
Jung Yoog Kang
Keyword(s):  
Differential Equations ◽  
Hermite Polynomials ◽  
Real Numbers ◽  
Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

scholarly journals MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Léo Pio-Lopez ◽  
Alberto Valdeolivas ◽  
Laurent Tichit ◽  
Élisabeth Remy ◽  
Anaïs Baudot
Keyword(s):  
Heterogeneous Networks ◽  
Heterogeneous Network ◽  
Link Prediction ◽  
Network Embedding ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Gene Associations ◽  
Different Types ◽  
Embedding Methods ◽  
Node Embeddings

AbstractNetwork embedding approaches are gaining momentum to analyse a large variety of networks. Indeed, these approaches have demonstrated their effectiveness in tasks such as community detection, node classification, and link prediction. However, very few network embedding methods have been specifically designed to handle multiplex networks, i.e. networks composed of different layers sharing the same set of nodes but having different types of edges. Moreover, to our knowledge, existing approaches cannot embed multiple nodes from multiplex-heterogeneous networks, i.e. networks composed of several multiplex networks containing both different types of nodes and edges. In this study, we propose MultiVERSE, an extension of the VERSE framework using Random Walks with Restart on Multiplex (RWR-M) and Multiplex-Heterogeneous (RWR-MH) networks. MultiVERSE is a fast and scalable method to learn node embeddings from multiplex and multiplex-heterogeneous networks. We evaluate MultiVERSE on several biological and social networks and demonstrate its performance. MultiVERSE indeed outperforms most of the other methods in the tasks of link prediction and network reconstruction for multiplex network embedding, and is also efficient in link prediction for multiplex-heterogeneous network embedding. Finally, we apply MultiVERSE to study rare disease-gene associations using link prediction and clustering. MultiVERSE is freely available on github at https://github.com/Lpiol/MultiVERSE.

Description of transient states of von Kármán vortex streets by low‐dimensional differential equations

1990 ◽  
Vol 2 (4) ◽  
pp. 479-481 ◽  
Author(s):  
F. Ohle ◽  
P. Lehmann ◽  
E. Roesch ◽  
H. Eckelmann ◽  
A. Hübler
Keyword(s):  
Differential Equations ◽  
Transient States ◽  
Von Karman ◽  
Vortex Streets ◽  
Karman Vortex ◽  
Low Dimensional ◽  
Von Kármán

scholarly journals Extracellular cytolysis by activated macrophages and granulocytes. I. Pharmacologic triggering of effector cells and the release of hydrogen peroxide.

1979 ◽  
Vol 149 (1) ◽  
pp. 84-99 ◽  
Author(s):  
C F Nathan ◽  
L H Brukner ◽  
S C Silverstein ◽  
Z A Cohn
Keyword(s):  
Trypan Blue ◽  
Response Curve ◽  
Target Cells ◽  
Activated Macrophages ◽  
Lymphoma Cells ◽  
Effector Cells ◽  
Proteose Peptone ◽  
Standard Assay ◽  
Different Types ◽  
J774 Cells

Lymphoma cells were rapidly lysed by activated macrophages and granulocytes in the presence of PMA. Release of 51Cr from lymphoma cells correlated closely with their destruction as viewed by scanning electron microscopy, and with reduction in the number of trypan blue-excluding cells. The standard assay involved 51 Cr release measured at 4.5 h, but injury appeared to be complete in 1 h. Of eight different types of effector cells tested, only those releasing abundant H2O2 in response to PMA were effective, that, is BCG-, C. parvum-, or casein-activated macrophages, or thioglycollate-elicited granulocytes. Normal macrophages, J774 cells, or macrophages elicited with thioglycollate broth or proteose-peptone were ineffective. BCG-activated macrophages and granulocytes caused 50% specific release of 51Cr from P388 lymphoma cells at E:T ratios between 1.4 and 4.5, and from mouse erythrocytes at E:T ratios of 0.017 to 0.025. 10 types of target cells varied widely in their susceptibility to lysis by reagent H2O2, with one-half maximal lysis occurring at H2O2 concentrations ranging from 3.63 X 10(-6) M to 3.85 X 10(-5) M. Effector cells were expected to generate approximately that much H2O2 during the period of injury. Susceptibility of the target cells to lysis by PMA-triggered granulocytes correlated closely with their sensitivity to H2O2 (r = 0.98). The membrane-active agents LPS and digitonin, which did not trigger H2O2 release, did not trigger cytotoxicity. The dose-response curve for triggering of H2O2 release by PMA was identical to that for triggering cytotoxicity. These results provided strong circumstantial evidence for the importance of H2O2 in extracellular cytolysis by activated macrophages and granulocytes when pharmacologically triggered.

CHAOS AND HYPERCHAOS IN A CLASS OF SIMPLE CELLULAR NEURAL NETWORKS MODELED BY O.D.E.

2006 ◽  
Vol 16 (09) ◽  
pp. 2729-2736 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Exponents ◽  
Cellular Neural Networks ◽  
New Class ◽  
Connection Matrices ◽  
Low Dimensional

This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer.

Synchronization of two coupled pacemaker cells based on the phase response curve

2009 ◽  
Vol 4 (1) ◽  
pp. 57-66
Author(s):  
Hossein Gholizade-Narm ◽  
Asad Azemi ◽  
Morteza Khademi ◽  
Masoud Karimi-Ghartemani
Keyword(s):  
Response Curve ◽  
Phase Response Curve ◽  
Phase Response ◽  
Pacemaker Cells
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