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Complexity theory has a certain universality in that, in Nature, we are surrounded by complex systems with nonlinear functions and interactions. Such systems have the property of evolving in a divergent way, but in a limited space. For example, the number of states that a chaotic system can achieve may or may not be limited, but the extreme values are in a limited space. Similarly, a fractal structure has a dimension represented by a real number, but this is within certain limits. For example, a quasi-volume has a real dimension between integers 2 and 3.

In all complex systems, there is a powerful intrinsic dynamic. The objective is to migrate a system to the border of chaos to turn it upside down and acquire new properties, which we have also called orders. Indeed, these systems evolve according to an internal dynamic in an unpredictable way (because they cannot be calculated) and converge towards an emerging global structure. These considerations therefore lead us to define the following schema of principle in which two totally different approaches to complex system management are included.

Figure 2.1. Two approaches to managing complex systems (from Pierre Massotte – HDR thesis, 1995)

These are in fact two visions of the world and two ways of understanding it:

 – on the left side of the figure, we find the Vitalist point of view, which is representative of the conventional approach to the processing of complex systems. A process is analyzed in a global and exhaustive way. By applying the principle of decomposition, the main, or global, tasks are divided into more elementary tasks and so on. The process is therefore modeled through a sequence of transformation functions. It is a static evolution model; by applying a stimulus, we observe and measure results. When the correct control parameters are adjusted, after a number of iterations or calculations, the real system can then be adjusted. We are in the old conception of a state of equilibrium dominated by the concept of action-reaction and predictability. In this static and top-down approach, we generally take the opportunity to simplify the so-called “complex” system or its process; it then becomes possible to automate it using computers. To solve a problem, many functions must be performed in parallel. The difficulty is only related to the performance of the calculation means, and it will always be possible, with appropriate time and investment, to find the right solution;

 – the right side of the figure represents the point of view of Mechanists and Connectionists. This is a dynamic, interaction-based approach, which we will call a bottom-up approach. Based on the principles just described, it is a question of generating a global function or of creating a structure or configuration based on the interactions existing in the interconnected network. This makes it possible to obtain a complex system (in the sense of behavior) from a great underlying simplicity (in terms of elementary functions and interactions). The implementation of such advanced concepts still raises many related problems nowadays, not to the performance of the calculation means, but to the overall performance of the emerging order (coherent with an overall objective). This requires an analysis of three points:- the exploitation of instabilities and low chaos to achieve optimal flexibility and responsiveness,- the definition of new associated methods for managing complex systems in order to better control them,- the development of new approaches and simulation tools to validate action plans to be applied to complex systems.

In practice, it would be a mistake to apply only one of the approaches described above. These complement each other and highlight a feedback loop that operates accurately and continuously. The above diagram taken as a whole (right and left sides) forms a dynamic structural whole: one the left, being reductionist, the diversity of the system is reduced while defining strategies and tactics (optimal action plans), while one the right, concerning new forms, configurations and orders are generated. The dynamic is therefore intrinsic and comes from the internal evolution of the whole.