American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Time-like surfaces of prescribed anisotropic mean curvature in Minkowski space
  • PROC Home
  • This Issue
  • Next Article
    Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains
2011, 2011(Special): 145-154. doi: 10.3934/proc.2011.2011.145

Drawing the output of dynamical systems by juxtaposing local outputs

Farida Benmakrouha 1, , Christiane Hespel 1, and  Edouard Monnier 1,

1. 

INSA-IRISA, 20 avenue des Buttes de Coesmes, 35043 Rennes cedex, France, France, France

Received  July 2010 Revised  June 2011 Published  October 2011

A dynamical system being described by its state equations and its initial state, we develop a method for drawing its output: It is based on the juxtaposition of local approximating outputs on successive time intervals $[t_i, t_(i+1)]0<=i<=n-1$. It consists in computing an approximated value of the state at initial point $t_i$ and an approximated output $y_i(t)$ on $[t_i, t_(i+1)]0<=i<=n-1$. An expression of the generating series $G_(q_r,t)$ for every component $q_r$ of the state $q$, an expression of the generating series $G_(y,t)$ of the output $y$ truncated at order $k$ are calculated and specified at every initial point $t_i$. We obtain an approximated output $y(t)$ at order $k$ in every interval $[t_i, t_(i+1)]0<=i<=n-1$. This method presents some theoretical advantages over Runge-Kutta methods: genericity, independency of the system and of the input, estimate of the error. So, an estimate of the suitable largest step can be computed. We have developed a Maple package for the creation of the generic expression of $G_(q_r,t),G_(y,t)$ and $y(t)$ at order $k$ and for the drawing of the local curves on every interval $[t_i, t_(i+1)]0<=i<=n-1$. For stable systems with oscillating output, for unstable systems near instability points, our method provides an appropriate result when a Runge-Kutta method is not suitable.
Keywords: symbolic algorithm, generating series, Curve drawing, oscillating output, dynamical system.
Mathematics Subject Classification: Primary: 37B55, 34C05; Secondary: 33F10, 34C1.
Citation: Farida Benmakrouha, Christiane Hespel, Edouard Monnier. Drawing the output of dynamical systems by juxtaposing local outputs. Conference Publications, 2011, 2011 (Special) : 145-154. doi: 10.3934/proc.2011.2011.145
[1]

Quoc T. Luu, Paul DuChateau. The relative biologic effectiveness versus linear energy transfer curve as an output-input relation for linear cellular systems. Mathematical Biosciences & Engineering, 2009, 6 (3) : 591-602. doi: 10.3934/mbe.2009.6.591
[2]

Wenjing Chen, Louis Dupaigne, Marius Ghergu. A new critical curve for the Lane-Emden system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (6) : 2469-2479. doi: 10.3934/dcds.2014.34.2469
[3]

Leong-Kwan Li, Sally Shao, K. F. Cedric Yiu. Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm. Journal of Industrial & Management Optimization, 2011, 7 (2) : 385-400. doi: 10.3934/jimo.2011.7.385
[4]

Hideo Ikeda, Masayasu Mimura, Tommaso Scotti. Shadow system approach to a plankton model generating harmful algal bloom. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 829-858. doi: 10.3934/dcds.2017034
[5]

Wen-Guei Hu, Song-Sun Lin. On spatial entropy of multi-dimensional symbolic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3705-3717. doi: 10.3934/dcds.2016.36.3705
[6]

H. M. Hastings, S. Silberger, M. T. Weiss, Y. Wu. A twisted tensor product on symbolic dynamical systems and the Ashley's problem. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 549-558. doi: 10.3934/dcds.2003.9.549
[7]

Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of first-order ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 281-298. doi: 10.3934/dcdsb.2014.19.281
[8]

Steven D. Galbraith, Ping Wang, Fangguo Zhang. Computing elliptic curve discrete logarithms with improved baby-step giant-step algorithm. Advances in Mathematics of Communications, 2017, 11 (3) : 453-469. doi: 10.3934/amc.2017038
[9]

Yūki Naito, Takasi Senba. Oscillating solutions to a parabolic-elliptic system related to a chemotaxis model. Conference Publications, 2011, 2011 (Special) : 1111-1118. doi: 10.3934/proc.2011.2011.1111
[10]

Nicolas Fournier. A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff. Kinetic & Related Models, 2019, 12 (3) : 483-505. doi: 10.3934/krm.2019020
[11]

Cheng Peng, Zhaohui Tang, Weihua Gui, Qing Chen, Jing He. A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019107
[12]

David Burguet, Todd Fisher. Symbolic extensionsfor partially hyperbolic dynamical systems with 2-dimensional center bundle. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2253-2270. doi: 10.3934/dcds.2013.33.2253
[13]

P.K. Newton. The dipole dynamical system. Conference Publications, 2005, 2005 (Special) : 692-699. doi: 10.3934/proc.2005.2005.692
[14]

Safya Belghith. Symbolic dynamics in nondifferentiable system originating in R-L-Diode driven circuit. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 275-292. doi: 10.3934/dcds.2000.6.275
[15]

Robert Stephen Cantrell, Suzanne Lenhart, Yuan Lou, Shigui Ruan. Preface on the special issue of Discrete and Continuous Dynamical Systems- Series B in honor of Chris Cosner on the occasion of his 60th birthday. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : i-ii. doi: 10.3934/dcdsb.2014.19.1i
[16]

Dorota Bors, Robert Stańczy. Dynamical system modeling fermionic limit. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 45-55. doi: 10.3934/dcdsb.2018004
[17]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701
[18]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure & Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249
[19]

Kuanysh A. Bekmaganbetov, Gregory A. Chechkin, Vladimir V. Chepyzhov, Andrey Yu. Goritsky. Homogenization of trajectory attractors of 3D Navier-Stokes system with randomly oscillating force. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2375-2393. doi: 10.3934/dcds.2017103
[20]

Yūki Naito, Takasi Senba. Bounded and unbounded oscillating solutions to a parabolic-elliptic system in two dimensional space. Communications on Pure & Applied Analysis, 2013, 12 (5) : 1861-1880. doi: 10.3934/cpaa.2013.12.1861

 Impact Factor: 

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences