Modeling and Control of Complex Dynamic Systems: Applied Mathematical Aspects

The paper considers work by Gardner and Ashby on the relationship between the connectivity of large systems and their stability, which suggests that all large complex dynamic systems will have a critical level of connectance beyond which they will go suddenly unstable. Further evidence by May on ecological systems supports this view. Reliability in systems, that is maintenance of stability of critical values over long periods of time, is held by Ashby to flow from such systems not being fully joined or connected. It is suggested that these considerations must apply also to attempts to plan and control the future of socioeconomic systems, both in relation to the planned system itself, and to the planning system which tries to invoke requisite variety to control the planned system. Stable systems in planning are thus seen as small, probably subsystemic in nature, not fully-joined, and hence hierarchical in structure. ‘Central’ planning results in instability because of size and complexity of control systems needed, and ‘equality’ is not a sustainable concept, as it requires or implies full connectedness. Finally, three kinds of system situations are put forward as representing gradations of stability and thus of ‘plannability’ or design possibility. These situations tend to show the limits of the plannable.

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Why Modeling Complex Dynamic Systems using Fuzzy Cognitive Maps?

International Journal of Business & Technology ◽

10.33107/ijbte.2017.5.2.05 ◽

2017 ◽

Vol 5 (2) ◽

pp. 1-7

Author(s):

Peter Groumpos

Keyword(s):

Dynamic Systems ◽

Cognitive Maps ◽

Difficult Problem ◽

Fuzzy Cognitive Maps ◽

Complex Dynamic ◽

Efficiency Criterion ◽

Efficient Operation ◽

Complex Dynamic Systems ◽

And Behavior ◽

And Control

The difficult problem of modeling Complex Dynamic Systems (CDS) is carefully reviewed. Main characteristics of CDS are considered and analyzed. Today’s mathematical models and approaches cannot provide satisfactory answers to the challenging problems of the society. The key problem of complex dynamic systems and control theory consists in the development of methods of qualitative analysis of the dynamics and behavior of such systems and in the construction of efficient control algorithms for their efficient operation. The purpose of control to bring the system to a point of its phase space which corresponds to maximal or minimal value of the chosen efficiency criterion is reviewed and analyzed. The reasons for using Fuzzy Cognitive Maps (FCMs) in modeling Complex dynamic Systems are provided. The basics of FCMs are briefly presented. An illustrative example is considered and interesting results are presented and discussed.

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