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Systems Theory

This chapter is an introduction to systems or systemic theory. The objective is to present the foundations of this theory, which are based on the notion of system. Indeed, systemic theory is based on the premise that everything can be considered a system, i.e. a complex network of interacting elements. The systemic approach is deeply conceptual, and we will see that the first concept is the notion of totality where the “whole” is more than the sum of the parts. Specifically, this means that the properties of an integrated system are not limited to the sum of the properties of the elements that constitute it. We also refer to a global or holistic approach, which is the basis of systemic theory. With this global approach, we seek to model the emergent properties of the system that arise from the complex cause-and-effect interactions between these elements. These interactions can be looped and provide feedback that may be stable or unstable. We also address circular causality.

1.1. The definition of a system

We will define a system in several ways, namely in a formal and normative way, in order to lay the theoretical foundations that will allow us to approach the next chapters of this book.

In a formal way, in Krob (2014), a system is characterized by (see Figure 1.4):

– a set of input flows X, output flows Y and internal states Q;

– as well as behaviors that link these inputs, outputs and states together over time.

Figure 1.1. A formal system (Krob 2014)

Among these behaviors, we have:

– a functional behavior that produces outputs y(t) belonging to Y from inputs x(t) belonging to X, from the current state q(t) belonging to Q;

– an internal behavior that changes the internal state q(t) belonging to Q over time under the action of an input x(t) belonging to X.

In a standardized way, a system is a combination of interacting elements organized to achieve one or more defined goals in an environment (ISO/IEC-15288: 2015 – see ISO (2015)).

In a detailed approach, a system is (Pollet 2016):

– an organized set of software, hardware and human components in mutual interaction;

– placed in a given environment: the environment consists of other systems;

– fulfilling a certain purpose: the system has a purpose;

– evolving over time to adapt to the loading of the environment and ensure this purpose.

This definition allows us to introduce the analysis of systems from two complementary points of view, which are the black box point of view and the white box point of view. Each of these views is studied from a structural, temporal and steering aspect (AFIS 2012).

We find in this definition the postulate that everything is a “system” (see Figure 1.5).

However, we will distinguish three families of systems (Meadows 2008; Hoarau 2010):

– simple systems: these are linear systems whose behavior is easily predictable;

– complicated systems: a set of simple systems that can be understood analytically;

– complex systems: these are nonlinear systems whose behavior is difficult to predict. They must therefore be understood as a whole and not by analytical decomposition.

Figure 1.2. Everything is a “system”

1.2. Definition of a complex system

To understand what a complex system is, we will compare it to a complicated system based on the work of Le Moigne (1999). A complicated system can be explained. Indeed, we can simplify it to discover its intelligibility in the sense of “explanation”. A complex system can also then be understood. Indeed, we must model it to build its intelligibility in the sense of “understanding”. This is not a definition of the complexity of a system, but it allows us to highlight the importance of modeling a complex system to understand it. However, a link can be made between the complexity of a system and the number of its internal and external interfaces. This increasing complexity is related to several parameters such as:

– the evolution of needs, which has led to an increase in the number of functions and therefore the number of components to be integrated;

– the evolution of technology;

– architecture choices: modular system or integrated system;

– the appearance of systems with leading software;

– critical systems (Cressent 2012).

In Meadows (2008), the author proposes a definition of complex systems as being nonlinear and difficult to predict.

Cause-and-effect links: indeed, a complex system is made of a set of networks of interactions with many cause-and-effect links.

Deadlines and delays: it has deadlines. This means that causes can have short-term effects or long-term effects.

Feedback loops: in interactions, it has feedback loops. These loops can be negative, i.e. they regulate the system by stabilizing it, or they can be positive, namely they amplify the effects leading to a divergence.

Emergent properties: the complex system has emergent properties, i.e. global properties that emerge from the interactions between its constituents. That is, the “whole”, i.e. the integrated system is more than the sum of its parts, its constituents.

Threshold effects: the complex system may have threshold factors. This means that there are thresholds above which the effects are different from those below the same thresholds.

Key factors: the complex system may have key factors. These are variables for which one cause can lead to great effects. This is what we call the “butterfly” effect.

1.3. Definition of a system of systems

Among the complex systems, we have a particular family that includes the systems of systems. The definition we can use is the following. It is a system that is composed of autonomous systems, i.e. systems that have their own objectives, and that collaborate with each other in order to meet a new need.

Figure 1.3. The Naval Aviation group: a system of systems

An example, which illustrates this definition, is the French Navy’s Naval Aviation group. Indeed, we have an anti-aircraft frigate, two anti-submarine warfare frigates and an SNA (nuclear attack submarine) that work together to form a new system whose mission is to defend the flagship, the aircraft carrier Charles de Gaulle (see Figure 1.3).

1.4. The systems approach

1.4.1. The reductionist approach

Engineering is made up of professions, which are called “disciplines”, for example, electrical engineering, mechanical engineering or computer engineering. The discipline approach is a specialist approach that is necessary but it gives a very “disabling” view of the system. This simplifying or reductive approach analyzes only a part of the system or at least according to a certain point of view, which depends on the discipline. This bottom-up view is called reductionist.

The reductionist vision is at the origin of the analytical approach which studies the system by breaking it down into increasingly detailed elements. This approach is perfectly adapted to systems, which can be decomposed into simple components without loss of information on their functioning (Meinadier 1998). However, in order to be applicable, the analytical approach makes two assumptions for the summability of the components to be possible. The first is that the interactions between the elements analyzed are negligible, and the second is that the relationships that express the behaviors of the elements are linear (von Bertalanffy 1968).

1.4.2. The holistic approach

The system engineer in charge of design must rely on this set of skills, but they must also have a more global vision of the product to be made. This approach allows the engineer to study the system in its environment and its external and internal interactions. The importance of such an approach lies in one of the fundamental properties of a system, which is its non-summability. Indeed, we cannot summarize the properties of a system to the sum of the properties of its elements. This global vision, from the top or “top down”, is called holistic.

The systemic approach is based on this holistic vision. It makes it possible to understand complex systems for which the only analytical approach cannot be adapted because it is too simplistic. Indeed, the analytical approach does not allow us to observe all the causal links between the system itself and its environment.

Since a complex system cannot be analyzed simply, the systems approach proposes to understand its behavior in its entirety by modeling and simulating it (Meinadier 1998). This is what Forrester’s system dynamics proposes in Forrester (1968), where the complex behaviors of a system are modeled by identifying and interacting with level (state) and flow variables.

Another characteristic of the analytical approach...