Non-linear Beatings as Non-stationary Synchronization of Weakly Coupled Autogenerators

2018 ◽  
pp. 53-83
Author(s):  
Margarita A. Kovaleva ◽  
Leonid I. Manevitch ◽  
Valery N. Pilipchuk
Keyword(s):  
Weakly Coupled ◽  
Non Linear

scholarly journals Earthquake sequencing: Chimera states with Kuramoto model dynamics on directed graphs

2015 ◽  
Vol 2 (1) ◽  
pp. 361-398
Author(s):  
K. Vasudevan ◽  
M. Cavers ◽  
A. Ware
Keyword(s):  
Markov Chain ◽  
Stress Field ◽  
Directed Graph ◽  
Directed Graphs ◽  
Kuramoto Model ◽  
Chimera States ◽  
Weakly Coupled ◽  
Non Linear ◽  
Field Fluctuations ◽  
The Kuramoto Model

Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model, and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress-interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behaviour of weakly-coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly-coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model to the non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behaviour of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and subsequently, point out the role of Kuramoto model in understanding the evolution of synchronous and asynchronous regions.

scholarly journals Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems

Algorithms ◽  
2017 ◽  
Vol 10 (4) ◽  
pp. 137
Author(s):  
Jorge Hernández-Gómez ◽  
Carlos Couder-Castañeda ◽  
Israel Herrera-Díaz ◽  
Norberto Flores-Guzmán ◽  
Enrique Gómez-Cruz
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Linear Dynamical Systems ◽  
Weakly Coupled ◽  
Non Linear

EXISTENCE AND STABILITY OF SOLITARY WAVES IN NON-LINEAR KLEIN–GORDON–MAXWELL EQUATIONS

2006 ◽  
Vol 18 (07) ◽  
pp. 747-779 ◽  
Author(s):  
EAMONN LONG
Keyword(s):  
Solitary Waves ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Topological Solitons ◽  
Weakly Coupled ◽  
Non Linear ◽  
Existence And Stability ◽  
Klein Gordon ◽  
Stability Of Solitary Waves

We prove the existence and stability of non-topological solitons in a class of weakly coupled non-linear Klein–Gordon–Maxwell equations. These equations arise from coupling non-linear Klein–Gordon equations to Maxwell's equations for electromagnetism.

Existence of positive entire solutions for weakly coupled semilinear elliptic systems

1992 ◽  
Vol 120 (1-2) ◽  
pp. 79-91 ◽  
Author(s):  
Yasuhiro Furusho
Keyword(s):  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Real Constant ◽  
Entire Solutions ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Weakly Coupled ◽  
Non Linear ◽  
Image Position

SynopsisWeakly coupled semilinear elliptic systems of the formare considered in RN, N≧2, where k = 1, 2, …, M, u = (u1, …, uM) and λ is a real constant. The aim of this paper is to give sufficient conditions for (*) to have entire solutions whose components are positive in RN and converge to non-negative constants as |x| tends to ∞. For this purpose a new supersolution-subsolution method is developed for the system (*) without any hypotheses on the monotonicity of the non-linear terms fk with respect to u.

scholarly journals Out of time ordered effective dynamics of a quartic oscillator

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Bidisha Chakrabarty ◽  
Soumyadeep Chaudhuri
Keyword(s):  
Effective Action ◽  
Thermal Noise ◽  
Stochastic Dynamics ◽  
Brownian Particle ◽  
Effective Theory ◽  
Thermal Bath ◽  
Effective Dynamics ◽  
Fluctuation Dissipation ◽  
Weakly Coupled ◽  
Non Linear

We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath’s 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle.

B. The Non-Linear Calculations for Pulsating Stars

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy
Keyword(s):  
Major Part ◽  
Afternoon Session ◽  
Discussion Session ◽  
Pulsating Stars ◽  
Fourth Symposium ◽  
Non Linear ◽  
Considerable Discussion ◽  
Informal Approach ◽  
Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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