    • 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

 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.
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
  Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020321  Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045  Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Salim A. Messaoudi. New general decay result for a system of viscoelastic wave equations with past history. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020273  Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020049  Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020467  Yichen Zhang, Meiqiang Feng. A coupled $p$-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075  Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216  Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020341  Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $\mathbb{R}^2$. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020447  Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020382  Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020468  Mathew Gluck. Classification of solutions to a system of $n^{\rm th}$ order equations on $\mathbb R^n$. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5413-5436. doi: 10.3934/cpaa.2020246

Impact Factor: