SDS2014 Guest Editorial

This special issue is devoted to collect developments in computational and theoretical methods for Dynamical Systems, their numerical approximation and their applications. This volume has grown out of some contributions presented during SDS2014 — 8th Workshop on Structural Dynamical Systems: Computational Aspects, the biannual workshop held in Capitolo-Monopoli Bari (Italy) 10–13 June 2014. This collection of papers describes some recent advances in the study of computational methods for structured dynamical systems and evidences the multi-disciplinary of this subject which spans basic and applied topics in math- ematics, numerical analysis, modeling and simulation. We believe the breadth of topics covered in this special issue will be useful to a wide readership interested in the very interesting and expanding research area of dynamical systems. The first contribution in the collections, the paper of Schönlein and Helmke, investigates the task of controlling ensembles of initial and terminal state vectors of parameter dependent linear systems by applying parameter-independent open loop controls. Using tools from complex approximation theory, necessary and sufficient conditions for ensemble controllability are established and a complete characterization of uniform ensemble controllability is also presented for a special class of ensembles. The second paper of Ironi and Tran deals with the algorithmic aspects of GRENS, a computational tool for qualitative simulation of the nonlinear and temporal multiscale dynamics of gene regulatory models. Algorithmic and implementation aspects of the proposed tool are detailed to simulate, from given initial conditions, all sound trajectories and to characterize qualitative properties of the gene regulatory system under consideration. The work of Berardi and Vurro proposes a new mechanism to solve the dynamical system governing the unsaturated water flow described by the Richards’ parabolic partial differential equation. Particularly, the proposed approach combines the method of lines with the ensemble Kalman filter (a data assimilation technique based on a Monte Carlo approach) to obtain a cheap numerical scheme for integrating in time the Richards’ equation, assuming that frequent corrections are guided by means of observations. The paper of Capobianco and Criscuolo focuses on new method for approximating two-dimensional weakly singular integrals. The proposed approach uses product quadrature rules based on suitable Jacobi zeros for evaluating the inner integral, related computational aspects are emphasized and the effectiveness of the proposed method is demonstrated on a classical aerodynamics problem. The article of Vermiglio presents some theoretical results on Abstract Delay Differential Equations which arise in many application fields and extend Delay Differential Equations from finite to infinite dimension. In the paper of Acciani, Di Modugno, Abrescia and Marano a numerical approach to integrate nonstationary Lyapunov matrix equation is presented to improve a stochastic linearization technique adopted for nonlinear systems representation. The proposed scheme is detailed and applied to solve the hysteretic Bouc-Wen model. The last two articles in this collection concentrate their attention on some aspects of the dynamics of some peculiar economic systems. The Orlando’s paper investigates chaotic behaviors within Kaldors framework, a model describing fluctuations of economic systems. Finally, the paper of Vandana and Sharma extends the Economic Order Quantity model with allowable partial backlogged shortages and analyzes how partial permissible delay-in-payment is linked to order quantity. To conclude the preface to this collection, we wish to thank the authors for their contributions and cooperation in preparing this Special Issue and the referees for their help in improving the submitted works. We are also grateful to the Editors-In-Chief of Mathematics and Computers in Simulation, Professor Christian Lécot and Professor Robert Beauwens, for having offered us the opportunity to present this volume and to France Pinon for the editorial help given during these months.