Search results for "linear system"

Wavelength selection of rippling patterns in myxobacteria

2016

Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them, and from contact signaling during bacterial collisions. Here we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al.\ [Proc. Natl. Acad. Sci. USA {\bf 98}, 14913 (2001) and Phys. Rev. E {\bf 70}, 041911 (2004)]. Bacteria in this model are phase oscillators with an extra internal phase through which they are coupled to a mean-field of oppositely moving bacteria. Previously, patterns for this model were obtaine…

Nonlinear trade-offs allow the cooperation game to evolve from Prisoner's Dilemma to Snowdrift.

2017

[EN] The existence of cooperation, or the production of public goods, is an evolutionary problem. Cooperation is not favoured because the Prisoner s Dilemma (PD) game drives cooperators to extinction. We have re-analysed this problem by using RNA viruses to motivate a model for the evolution of cooperation. Gene products are the public goods and group size is the number of virions co-infecting the same host cell. Our results show that if the trade-off between replication and production of gene products is linear, PD is observed. However, if the trade-off is nonlinear, the viruses evolve into separate lineages of ultra-defectors and ultra-cooperators as group size is increased. The nonlinear…

Adaptive synchronization of master-slave systems with mixed neutral and discrete time-delays and nonlinear perturbations

2011

This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effe…

Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere

1997

We determine within an accuracy of ∼10% the absolute magnitude of the quadratic effective coefficients of types I and II phase-matched second-harmonic generation from conversion efficiency measurements in a single nonlinear crystal cut as a sphere. The agreement is good with measurements performed in thin parallelepipedal samples. The material studied is KTiOPO4, for which improved Sellmeier equations are given.

Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound lev…

2011

Abstract This paper experimentally investigates the holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels. The theoretical formulations are based on a semi-empirical approach and the use of Fok’s function to model the acoustic surface impedance. For the high sound level regime, an empirical power law involving three coefficients is adapted. It is shown theoretically and experimentally that these coefficients can lead to optimized absorption performance and particularly, a formula relating the critical Reynolds number (Reynolds number value after which the absorption coefficient decreases with the increase of sound level) a…

2014

In this paper mathematical modeling of a vehicle crash test based on a single-mass is studied. The model under consideration consists of a single-mass coupled with a spring and/or a damper. The parameters for the spring and damper are obtained by analyzing the measured acceleration in the center of gravity of the vehicle during a crash. A model with a nonlinear spring and damper is also proposed and the parameters will be optimized with different damper and spring characteristics and optimization algorithms. The optimization algorithms used are interior-point and firefly algorithm. The objective of this paper is to compare different methods used to establish a simple model of a car crash an…

Modelling infiltration by means of a nonlinear fractional diffusion model

2006

The classical Richards equation describes infiltration into porous soil as a nonlinear diffusion process. Recent experiments have suggested that this process exhibits anomalous scaling behaviour. These observations suggest generalizing the classical Richards equation by introducing fractional time derivatives. The resulting fractional Richards equation with appropriate initial and boundary values is solved numerically in this paper. The numerical code is tested against analytical solutions in the linear case. Saturation profiles are calculated for the fully nonlinear fractional Richards equation. Isochrones and isosaturation curves are given. The cumulative moisture intake is found as a fun…

Linear and nonlinear interest rate exposure in Spain

2010

PurposeThis paper aims to carry out a comprehensive analysis of the influence of interest rate risk on Spanish firms at the industry level.Design/methodology/approachThe methodology employed has its origin in the two‐index linear regression model proposed by Stone. This traditional interest rate exposure model has been extended in this paper to allow for a nonlinear exposure component as well as the presence of asymmetric behaviour in the exposure pattern.FindingsInterest rate exposure is not homogeneous for all the Spanish industries. In line with other markets, highly leveraged industries (construction and real estate), regulated industries (electrical and utilities), and banking industry…

Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Comm…

2019

In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive com…

Fuzzy modeling and control for a class of inverted pendulum system

2014

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/936868 Open Access Focusing on the issue of nonlinear stability control system about the single-stage inverted pendulum, the T-S fuzzy model is employed. Firstly, linear approximation method would be applied into fuzzy model for the single-stage inverted pendulum. At the same time, for some nonlinear terms which could not be dealt with via linear approximation method, this paper will adopt fan range method into fuzzy model. After the T-S fuzzy model, the PDC technology is utilized to design the fuzzy controller secondly. Numerical simulation res…