A stability index for travelling waves in activator-inhibitor systems

2019 ◽  
Vol 150 (1) ◽  
pp. 517-548
Author(s):  
Paul Cornwell ◽  
Christopher K. R. T. Jones
Keyword(s):  
Eigenvalue Problem ◽  
Symplectic Form ◽  
Travelling Waves ◽  
Stability Index ◽  
Maslov Index ◽  
Evans Function ◽  
Conjugate Points ◽  
Spatial Evolution ◽  
The Stability ◽  
Activator Inhibitor

AbstractWe consider the stability of nonlinear travelling waves in a class of activator-inhibitor systems. The eigenvalue equation arising from linearizing about the wave is seen to preserve the manifold of Lagrangian planes for a nonstandard symplectic form. This allows us to define a Maslov index for the wave corresponding to the spatial evolution of the unstable bundle. We formulate the Evans function for the eigenvalue problem and show that the parity of the Maslov index determines the sign of the derivative of the Evans function at the origin. The connection between the Evans function and the Maslov index is established by a ‘detection form,’ which identifies conjugate points for the curve of Lagrangian planes.

scholarly journals Evans function computation for the stability of travelling waves

2018 ◽  
Vol 376 (2117) ◽  
pp. 20170184 ◽  
Author(s):  
B. Barker ◽  
J. Humpherys ◽  
G. Lyng ◽  
J. Lytle
Keyword(s):  
Travelling Waves ◽  
Evans Function ◽  
Detonation Waves ◽  
Model Parameters ◽  
Theme Issue ◽  
Function Computation ◽  
Computational Aspects ◽  
The Stability ◽  
Linearized Operator

In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

A FORECAST OF PRODUCTIVE LONGEVITY OF HOLSTEIN COWS BY INDIRECT SIGNS

2020 ◽  
Author(s):  
З.С. САНОВА
Keyword(s):  
Correlation Coefficient ◽  
Aging Process ◽  
Direct Relationship ◽  
Stability Index ◽  
Age At First Calving ◽  
Group I ◽  
Predicted Values ◽  
The Stability ◽  
Relationship Of ◽  
The Relationship

В статье представлены материалы о взаимосвязи продолжительности продуктивного использования коров с характеристикой устойчивости к деградации, с возрастом отела и удоем. В исследованной, разнородной по происхождению, группе животных для прогноза продуктивного периода коров, обусловленного устойчивостью к деградации и возрастом первого отела, пригодно уравнение регрессии, аргументами в котором являются индекс устойчивости, возраст первого отела в первой и второй степенях. Коэффициент корреляции межу предсказанными значениями продуктивного периода и его фактическими величинами в I группе составляет 0,502, во II - 0,604. При этом крайние варианты прогнозируются со статистическими ошибками 5 мес при оценке индекса устойчивости по 2 лактациям и 4,1 мес по 3, а средние варианты, соответственно, 1,6 и 1,51 мес. Индекс устойчивости к процессу старения является важной характеристикой биологических особенностей коров, определяющий их продуктивное долголетие. Его оценка по первым 2 и 3 лактациям имеет прямолинейную связь с продуктивным периодом (r=0,4109 и r=0,5270), соответственно. Зависимость продуктивного периода от возраста первого отела криволинейная — с увеличением возраста первого отела сокращается срок продуктивного использования, при возрасте первого отела более 1400 дней срок продуктивного использования колеблется от 1,33 до 1,41 лактации. Коэффициент корреляции между этими характеристиками коров составляет - 0,2164 в I и - 0,2620 во II группах. The article presents materials about the relationship of the duration of productive use of cows with the characteristic of resistance to degradation, with the age of calving and milk yield. In the studied group of animals, which is heterogeneous in origin, the regression equation is suitable for predicting the productive period of cows due to resistance to degradation and the age of the first calving, the arguments of which are the stability index, the age of the first calving in the first and second degrees. The correlation coefficient between the predicted values of the productive period and its actual values in group I is 0.502, in group II - 0.604. At the same time, the extreme variants are predicted with statistical errors of 5 months when evaluating the stability index for 2 lactations and 4.1 months for 3, and the average variants, respectively, are 1.6 and 1.51 months. The index of resistance to the aging process is an important characteristic of the biological characteristics of cows, which determines their productive longevity. Its estimate for the first 2 and 3 lactations has a direct relationship with the productive period (r=0.4109 and r=0.5270), respectively. The dependence of the productive period age at first calving curvilinear with increasing age at first calving reduces the time to productive use, while age at first calving of more than 1400 days, the period of productive use ranges from 1.33 to 1.41 lactation. The correlation coefficient between these characteristics of cows is-0.2164 in I and-0.2620 in II groups.

scholarly journals The stability index of a cactus

1977 ◽  
Vol 24 (2) ◽  
pp. 170-183
Author(s):  
Douglas D. Grant ◽  
D. A. Holton
Keyword(s):  
Connected Graph ◽  
Stability Index ◽  
The Stability

AbstractWe show that ifGis a connected graph of ordernsuch that no line lies in more than one cycle (in other words,Gis a cactus of ordern), then the stability index ofGis one of the integers 0, 1,n−7,n−6,n−5,n−4 orn.

Features of pubertal patients with schizophrenia neurocognitive profile

2017 ◽  
Vol 41 (S1) ◽  
pp. S430-S431
Author(s):  
Y. Barylnik ◽  
S. Pakhomova ◽  
D. Samoylova ◽  
J. Abrosimova ◽  
E. Kolesnichenko ◽  
...  
Keyword(s):  
Stability Index ◽  
Neurocognitive Disorders ◽  
Motor Speed ◽  
Structuring Element ◽  
Test Part ◽  
Psychic Disorders ◽  
Competing Interest ◽  
Neurocognitive Profile ◽  
The Stability ◽  
High Level

Identifying the patterns of neurocognitive disorders in pubertal schizophrenia is actual.MethodsBenton Test of visual retention, methods of forward and reverse bills, Bourdon correction sample, Wechsler's subtests (subtest 11 – “Encryption”, subtest 12 – “Labyrinths” 1, 2, 3, 4, 5), Trail Creating a Test Part A.ResultsAll patients were divided into 3 groups. The first group (schizophrenia) and second group (other psychic disorders) showed the worst results than healthy subjects. Qualitative analysis of the “Benton Test” results showed similar variations of difficulty and types of errors in the subjects of the first and second groups – ignoring the number of the figure sides, as well as difficulties in the structuring element of the image corners. The “Methods of forward and reverse bills” demonstrated the fatigue and attention instability. “Bourdon test” showed a high level of the stability index (K = 0.09). Wechsler's subtest “Encryption B” obtained poor results, indicating a pathological decrease in visual-motor speed. During the subtest “Labyrinths 1, 2, 3, 4, 5” the subjects of first and second groups exceeded the allowable time limit, but the first group of schizophrenia patients allowed more blunders during pubertal study (ignored the walls of the maze, torn pencil despite the given instructions). The test groups 1 and 2 while passing “Trail Creating a Test Part A” have shown good results – job data did not cause difficulties and carried out in accordance with the specified instructions.ConclusionsNeurocognitive disorders allow to confirm the presence of morphological and functional brain changes when endogenous mental illness occurs.Disclosure of interestThe authors have not supplied their declaration of competing interest.

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

THE OASIS SOIL TYPE CHANGE AND ITS FRACTAL IN MANASI RIVER BASIN BETWEEN 1987–2006, ARID NORTHWESTERN CHINA / MANASI UPĖS BASEINO SAUSRINGOJE ŠIAURĖS VAKARŲ KINIJOJE OAZIŲ DIRVOŽEMIO TIPŲ POKYČIAI IR FRAKTALAI 1987–2006 M

2012 ◽  
Vol 20 (3) ◽  
pp. 177-184 ◽  
Author(s):  
Pujia Yu ◽  
Hailiang Xu ◽  
Shiwei Liu ◽  
Xinfeng Zhao ◽  
Qingqing Zhang ◽  
...  
Keyword(s):  
River Basin ◽  
Soil Type ◽  
Stability Index ◽  
Rapid Expansion ◽  
Soil Types ◽  
Semiarid Region ◽  
Arid Northwestern China ◽  
Type Change ◽  
The Stability ◽  
Soil Changes

During the past 20 years, great landscape changes took place in the northwest of China. Landscape change resulted in soil type transformations. This paper discusses the changes and fractal of soil types in oasis. In order to do it, the soil type maps of Manasi River Basin in 1987 and 2006 were used. 13 types of soil and 2 types of land-use were classified and analyzed in the study area. Results indicated many variations in characteristics. Firstly, all soil types underwent remarkable changes from 1987 to 2006 in the study area: the identified changed area was about 30% or 6506.33 km2. Secondly, in comparison with 1987, in 2006 2/3 of the area's soil types increased, while 1/3 decreased. Rapid expansion of Aquicambids (415.28 km2), and rapid decrease of Petrocambids (797.05 km2) and Aquisalids (415.93 km2) were the noticeable findings. Furthermore, Haplocambids obtained largest gains from other soil types, while Petrocambids lost largest area to other types. Additionally, the fractal relationship objectively existed between the perimeter and area of soil patches. The fractal dimension of Aquisalids, Petrocalcids and Ustifluvents became higher and their shapes became more complex during this period. The stability index was higher in 2006 which indicated that the spatial structure of soil type was more stable than in 1987. These chaotic and occasional changes were largely caused by human activities and natural conditions. Consequently, environmental managers should pay more attention to soil changes in the arid and semiarid region. Santrauka Per pastaruosius 20 metų šiaurės vakarų Kinijoje įvyko didelių kraštovaizdžio pokyčių, lėmusių ir dirvožemio tipų pakitimus. Remiantis 1987–2006 m. Manasi upės baseino dirvožemio žemėlapiais, aptariami dirvožemio tipų pokyčiai ir fraktalai oazėse. Pasirinktoje teritorijoje išskirta ir analizuota 13 dirvožemio tipų ir dvejopa žemėnauda. Nustatyta daug kintamųjų parametrų. Pirma, tirtõs teritorijos visų tipų dirvožemiai nuo 1987 iki 2006 m. žymiai pakito. Nustatytoji pokyčių zona apima apie 30 % teritorijos, arba 6 506,32 km2. Antra, palyginti su 1987 m., 2006 m. 10 dirvožemio tipų teritorija padidėjo, o 5 tipų sumažėjo. Sparčiai padidėjo Aquicambids (415,28 km2), sparčiai sumažėjo Petrocambids (797,05 km2) ir Aquisalids (415,93 km2), pokyčiai buvo žymūs. Iš visų kitų pakitusių dirvožemių tipų Haplocambids plotai padidėjo daugiausia, o labiausiai, palyginti su kitais, sumažėjo Petrocambids plotai. Be to, pastebėta, kad tarp dirvožemio teritorijos plotų ir perimetrų objektyviai egzistuoja fraktalinės sąsajos. Fraktalinės dimensijos Aquisalids, Petrocalcids ir Ustifluvents per minėtą laikotarpį padidėjo, o jų formos tapo sudėtingesnės. Stabilumo indeksas 2006 m. buvo didesnis. Tai rodė, kad erdvinė dirvožemio struktūra mažai pakito, tapo stabilesnė, palyginti nei buvo 1987 m. Šiuos atsitiktinius pokyčius iš esmės lėmė žmogaus veikla ir gamtinės sąlygos. Prieita prie išvados, kad sausojo ar pusiau sauso klimato regionuose kraštotvarkos vykdytojai dirvožemio pokyčiams turėtų skirti daugiau dėmesio.

Densities of scaling limits of coupled continuous time random walks

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marcin Magdziarz ◽  
Tomasz Zorawik
Keyword(s):  
Fractional Differential Equations ◽  
Continuous Time ◽  
Stability Index ◽  
Scaling Limits ◽  
Explicit Formulas ◽  
Material Derivative ◽  
Lévy Walks ◽  
Continuous Time Random Walks ◽  
Fractional Differential ◽  
The Stability

AbstractIn this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer

scholarly journals Neural Entrainment Meets Behavior: The Stability Index as a Neural Outcome Measure of Auditory-Motor Coupling

2021 ◽  
Vol 15 ◽  
Author(s):  
Mattia Rosso ◽  
Marc Leman ◽  
Lousin Moumdjian
Keyword(s):  
Outcome Measure ◽  
Pathological Condition ◽  
Brain Activity ◽  
Behavioral Outcomes ◽  
Stability Index ◽  
Behavioral Measures ◽  
Neural Entrainment ◽  
Entrainment Effect ◽  
The Stability ◽  
The Impact

Understanding rhythmic behavior in the context of coupled auditory and motor systems has been of interest to neurological rehabilitation, in particular, to facilitate walking. Recent work based on behavioral measures revealed an entrainment effect of auditory rhythms on motor rhythms. In this study, we propose a method to compute the neural component of such a process from an electroencephalographic (EEG) signal. A simple auditory-motor synchronization paradigm was used, where 28 healthy participants were instructed to synchronize their finger-tapping with a metronome. The computation of the neural outcome measure was carried out in two blocks. In the first block, we used Generalized Eigendecomposition (GED) to reduce the data dimensionality to the component which maximally entrained to the metronome frequency. The scalp topography pointed at brain activity over contralateral sensorimotor regions. In the second block, we computed instantaneous frequency from the analytic signal of the extracted component. This returned a time-varying measure of frequency fluctuations, whose standard deviation provided our “stability index” as a neural outcome measure of auditory-motor coupling. Finally, the proposed neural measure was validated by conducting a correlation analysis with a set of behavioral outcomes from the synchronization task: resultant vector length, relative phase angle, mean asynchrony, and tempo matching. Significant moderate negative correlations were found with the first three measures, suggesting that the stability index provided a quantifiable neural outcome measure of entrainment, with selectivity towards phase-correction mechanisms. We address further adoption of the proposed approach, especially with populations where sensorimotor abilities are compromised by an underlying pathological condition. The impact of using stability index can potentially be used as an outcome measure to assess rehabilitation protocols, and possibly provide further insight into neuropathological models of auditory-motor coupling.

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