Development of methods for modelling complex ecological systems

In modelling complex ecological systems

• 1.(i) a new theory of diffusion of non-conservative particles,
• 2.(ii) procedures for aggregation and averaging of ecosystem components with subsequent hierarchical decomposition and for
• 3.(iii) joint analysis of dynamic and logical informational models were developed and shortly described.

Numerical procedures support the elaboration of prognoses about the behaviour of men-controlled ecological systems. Some results in modelling the North-West Black Sea shelf ecosystem are demonstrated.     

An overview of approximation methods for large-scale dynamical systems

Methods for the approximation of large-scale dynamical systems will be surveyed. There are mainly two families namely, the SVD-based and Krylov-based approximation methods. The former family is based on the singular value decomposition and the second on moment matching. While the former has many desirable properties including an error bound, it cannot be applied to systems of high complexity. The strength of the latter on the other hand, is that it can be implemented iteratively and is thus appropriate for application to high complexity systems. An effort to combine the best attributes of these two families leads to a third class of approximation methods, which will be referred to as SVD/Krylov. Following a survey of these methods we will conclude with a new result concerning model reduction with preservation of passivity which is appropriate for application to large-scale circuits arising in VLSI chip performance verification.     

Nonlinear Galerkin methods for the model reduction of nonlinear dynamical systems

Numerical simulations of large nonlinear dynamical systems, especially over long-time intervals, may be computationally very expensive. Model reduction methods have been used in this context for a long time, usually projecting the dynamical system onto a sub-space of its phase space. Nonlinear Galerkin methods try to improve on this by projecting onto a sub-manifold which does not have to be flat. These methods are applied to the finite element model of a wind-turbine, where both the mechanical and the aerodynamical degrees of freedom can be considered for model reduction. For the internal forces (moments, section forces) the nonlinear Galerkin method gives a considerable increase in accuracy for very little computational cost.     

Scilab software package for the study of dynamical systems

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE.

Program summary

Program title: ChaosCatalogue identifier: AEAP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 885No. of bytes in distributed program, including test data, etc.: 5925Distribution format: tar.gzProgramming language: Scilab 3.1.1Computer: PC-compatible running Scilab on MS Windows or LinuxOperating system: Windows XP, LinuxRAM: below 100 MegabytesClassification: 6.2Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE).Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies.Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem.Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.     

Comparisons of practical hierarchical control methods for interconnected dynamical systems

This paper gives a brief survey of possible methods which can be used for the practical control of large interconnected dynamical systems. The development is in two parts, i.e. optimal methods and suboptimal methods. In the first part, a brief outline is given of infeasible methods like Goal co-ordination and the Takara-Sage algorithm. In the general study of infeasible methods, Tamura's three-level method, Tamura's time-delay method and Pearson's pseudo-model co-ordination method are also included. It is seen that both the algorithms of Tamura as well as the Takahara-Sage method are particularly suited to systems with slow dynamics whereas Pearson's pseudo-model co-ordination method could be used advantageously for systems with fast dynamics.A practical example is then given of optimal traffic control using an infeasible method, in this case the time-delay method of Tamura. The main conclusion to emerge from this part is that optimal methods will require multiple processors for on-line dynamic optimization although for systems with slow dynamics like the traffic example, fairly large problems could nevertheless be tackled using only one processor.There are certain classes of systems for which it may be possible to obtain virtually optimal control using only a single processor even when the number of subsystems is very large. One such class of problems is of serially connected dynamical systems. In the second part of this paper a suboptimal approach is described for the control of serial systems and the method is demonstrated using river pollution as an example. Finally, a new method is developed which enables a significant improvement to be made for serial systems with conflicts between the subsystems and an example illustrates this approach.     

Optimizing quasilinear stochastic dynamical systems with complex structure

We propose a generalization and a specification of our results for synthesizing optimal trajectories in control problems for quasilinear stochastic dynamical systems of diffuse type. Information constraints imposed on the system are reflected in the fact that each component of the control strategy may depend only on a preselected subset of exactly measured components of the state vector. We give specific algorithms to find the control in each case of information constraints. As an example, we consider the orbit stabilization for a man-made Earth satellite.     

Doubly-indexed dynamical systems: State-space models and structural properties

Doubly-indexed dynamical systems provide a state space realization of two-dimensional filters which includes previous state models. Algebraic criteria for testing structural properties (reachability, observability, internal stability) are introduced.This work was supported by CNR-GNAS     

An argument-principle-based framework for structural and spectral characteristics in linear dynamical systems

By means of the argument principle in complex analysis, the paper proposes a novel complex geometric framework about structural features in terms of controllability/observability and stability/stabilisability, and spectral ones in terms of bounded/positive realness for transfer functions in linear dynamical systems. The proposed criteria render alternative complex/frequency-domain interpretations about the structural and spectral essentials. Moreover, the criteria are implementable graphically with locus plotting, independent of singularities distribution, locus orientation specification, singularity-related locus encirclement counting and prior frequency sweeping; the criteria are also utilisable numerically via complex argument increment integration without locus plotting, independent of iterative algorithms. In either ways, the criteria are numerically tractable and opt for robustness analysis and synthesis. Numerical examples are included to illustrate the main results.     

A criterion for structural stability of quadruples of matrices defining generalized dynamical systems

A characterization in terms of the rank of a matrix is proved for structurally stable quadruples related to generalized dynamical systems

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under a local equivalence relation by realizing a geometric approach.     

Topology of the moduli space for reachable linear dynamical systems: The complex case

This paper deals with the algebraic topology of the space _n,m of complex reachable linear dynamical systems. Topological invariants such as the singular homology groups of _n,m are explicitly computed and they are shown to coincide with those of a certain Grassmann manifold. From this some new results on the topology of rational transfer matrices with fixed McMillan degree are obtained.     

Visual-FIR: A tool for model identification and prediction of dynamical complex systems

A new platform for the fuzzy inductive reasoning (FIR) methodology has been designed and developed under the MATLAB environment. The new tool, named Visual-FIR, allows the identification of dynamic systems models in a user-friendly environment. FIR offers a pattern-based approach to modeling and predicting either univariate or multivariate time series, obtaining very good results when applied to various areas such as control, biology, and medicine. However, the available implementation of FIR was such that new code had to be developed for each new application studied. Visual-FIR resolves this limitation and offers a high-efficiency implementation. Furthermore, the Visual-FIR platform presents a new vision of the methodology based on process blocks and adds new features, increasing the overall capabilities of the FIR methodology. The DAMADICS benchmark problem is addressed in this research using the Visual-FIR approach.     

Development methods for trusted computer systems

Conclusion Well-designed computer systems can be safer than hardwired alternatives, and computer systems can control processes which are too complex for hardwired solutions, or where the hardwired solution is uneconomic.     

On evolution of open dynamical systems: Some algebraic methods

Open dynamical systems which are governed by a finite number of ordinary differential equations with controls (time-dependent control parameters) constitute a large and important class of models for practical purposes. In the last few years, there has been considerable interest and progress in algebraic methods for solving the equations of the form (*) $$\dot x\left( t \right) = L_0 x\left( t \right) + \sum\limits_{j = 1}^r {u\left( t \right)L_i x\left( t \right)} ,$$ i.e. bilinear models. In this paper, intended as an expository introduction to the main results of system-theoretic approach to the modelling of open systems, a new “polynomial” representation of solutions to (*) is discussed.     

A new version of Scilab software package for the study of dynamical systems

This work presents a new version of a software package for the study of chaotic flows, maps and fractals [1]. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well-known examples are implemented, with the capability of the users inserting their own ODE or iterative equations.

New version program summary

Program title: Chaos v2.0Catalogue identifier: AEAP_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1275No. of bytes in distributed program, including test data, etc.: 7135Distribution format: tar.gzProgramming language: Scilab 5.1.1. Scilab 5.1.1 should be installed before running the program. Information about the installation can be found at http://wiki.scilab.org/howto/install/windows.Computer: PC-compatible running Scilab on MS Windows or LinuxOperating system: Windows XP, LinuxRAM: below 150 MegabytesClassification: 6.2Catalogue identifier of previous version: AEAP_v1_0Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788Does the new version supersede the previous version?: YesNature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE).Solution method:

1.

Numerical solving of ordinary differential equations for the study of chaotic flows. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincare sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies.

2.

Numerical solving of iterative equations for the study of maps and fractals.

Reasons for new version: The program has been updated to use the new version 5.1.1 of Scilab with new graphical capabilities [2]. Moreover, new use cases have been added which make the handling of the program easier and more efficient.Summary of revisions:

1.

A new use case concerning coupled predator-prey models has been added [3].

2.

Three new use cases concerning fractals (Sierpinsky gasket, Barnsley's Fern and Tree) have been added [3].

3.

The graphical user interface (GUI) of the program has been reconstructed to include the new use cases.

4.

The program has been updated to use Scilab 5.1.1 with the new graphical capabilities.

Additional comments: The program package contains 12 subprograms.

•

interface.sce - the graphical user interface (GUI) that permits the choice of a routine as follows

•

1.sci - Lorenz dynamical system

•

2.sci - Chua dynamical system

•

3.sci - Rosler dynamical system

•

4.sci - Henon map

•

5.sci - Lyapunov exponents for Lorenz dynamical system

•

6.sci - Lyapunov exponent for the logistic map

•

7.sci - Shannon entropy for the logistic map

•

8.sci - Coupled predator-prey model

•

1f.sci - Sierpinsky gasket

•

2f.sci - Barnsley's Fern

•

3f.sci - Barnsley's Tree

Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE, Lyapunov exponents calculation and fractals.References:

[1]

C.C. Bordeianu, C. Besliu, Al. Jipa, D. Felea, I. V. Grossu, Comput. Phys. Comm. 178 (2008) 788.

[2]

S. Campbell, J.P. Chancelier, R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer, 2006.

[3]

R.H. Landau, M.J. Paez, C.C. Bordeianu, A Survey of Computational Physics, Introductory Computational Science, Princeton University Press, 2008.

     

Representations and test planning methods for complex technical systems

The paper examines the applicability of standard experimental design methods to the set of representations of complex technical systems. A functional-decomposition method and a functional test planning method are developed for complex technical systems.Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–46, March–April, 1992.     

平行系统方法与复杂系统的管理和控制

提出平行系统方法的基本思想、概念和运行的基本框架，并讨论了控制系统与平行系统的关系和异同之处，平行系统是控制系统和计算机仿真随着系统复杂程度的增加以及计算技术和分析方法的进一步发展而必然迈上的一个更高的台阶，是弥补很难甚至无法对复杂系统进行精确建模和实验之不足的一种有效手段，也是对复杂系统进行管理和控制的一种可行方式。     

Solution or reduction of equilibrium equations for large complex structural systems

A general purpose subprogram is presented for the solution or partial reduction of a set of equilibrium equations. The subroutine can be used as an efficient tool for the direct solution of a complex structural system or to form a reduced stiffness matrix for a large substructure. The numerical method is based on the active column method in which the stiffness matrix is stored in compacted block form on secondary storage. Therefore, the maximum size of system which can be solved is generally governed by the amount of secondary storage available at a particular computer facility. The subprogram presented is in the form of three main Fortran subroutines which separate the block manipulation from the arithmetic logic and the operations associated with secondary storage units. Hence, machine dependent subroutines can easily be added in order to increase the efficiency for arithmetic operations and for direct access to secondary storage units.