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In the previous chapter, we saw that nonlinear dynamical systems (NLDS) are subject to complex behaviors. They are “programmable networks” whose functions and interactions are not necessarily linear. We encounter them in all fields: industrial, financial, economic, social, political, etc.

When we have qualitative systems, it is relatively easy to build a mathematical model of the phenomenon or system evolution, to evaluate it and study its behavior. When we have quantitative information, the development of the model is much more difficult; so is the study of the model.

In a manufacturing system dedicated to the assembly and testing of complex technological sets, the problem is what will determine the quality of the product and the performance of the manufacturing process: “will it remain stable? Will productivity be optimal? Does the production system remain under control?” So many questions that a production manager asks himself or herself.

First, it should be noted that in a conventional system, most tasks are often performed directly. These same tasks to be performed are under the control of a human being and several elements must be taken into account to characterize the level and nature of an organization in which human resources are involved, namely:

 – Competences: these are linked to a constituent entity of a system and correspond to a task, function or mission entrusted to it. Competences refer to concepts such as aptitude, talents, skill, knowledge and experience or know-how necessary to ensure the successful completion of this task. These are the competences, available at the level of an entity, that will bring added value to the product or service being transformed. In the context of this study, competency is strongly correlated with the autonomy of this entity.

 – Culture: this refers to all the uses, traditions and customs, shared beliefs and convictions, ways of seeing, doing and knowing how to that ensure an implicit code of behavior and cohesion within a system or organization. As we can see, the cohesion of a system implies that a certain number of entities are linked together in order to form a network. The cohesion of the network is then ensured by links and interactions.

 – Emulation and motivation: the first term refers to a state of mind or willingness to equal or surpass someone or something. Similarly, motivation is a process that triggers, continues or stops a behavior. These two concepts are used to express the activation or inhibition of a link, the reinforcement or not of an action or interaction.

The functioning and behavior of such an organization depends of course on these three elements and their combination. The French mathematician René Thom examined this problem through his theory of “catastrophes”, which allowed him to highlight transition phenomena and discontinuities, of which we will mention only two examples:

 – the distribution of competences and the communication system between groups of operators are fundamental. Some imbalances always end up resulting in an explosion or implosion of behavior, which inevitably has an impact on the result;

 – the interactions that condition the feedback effects are essential. Similarly, the interaction force will be the result of learning sessions, progressive and iterative reinforcement or inhibition of links between entities.