Simulating Complex Systems
Complex System Theories, Their Behavioural Characteristics and Their Simulation
Rabia Aziza
, Amel Borgi
, Hayfa Zgaya
and Benjamin Guinhouya
LIPAH Research Laboratory, Université de Tunis El Manar, Rommana 1068, Tunis, Tunisia
EA 2994, Public Health: Epidemiology and Healthcare Quality, University Lille,
42 Rue Ambroise Paré, Loos 59120, Lille, France
Keywords: Complex Systems, Simulation, Agents, Constructivist Approach.
Abstract: Complexity science offers many theories such as chaos theory and coevolutionary theory. These theories
illustrate a large set of real life systems and help decipher their nonlinear and unpredictable behaviours.
Categorizing an observed Complex System among these theories depends on the aspect that we intend to
study, and it can help better understand the phenomena that occur within the system. This article aims to give
an overview on Complex Systems and their modelling. Therefore, we compare these theories based on their
main behavioural characteristics, e.g. emergence, adaptability, and dynamism. Then we compare the methods
used in the literature to model and simulate Complex Systems, and we propose and discuss simple guidelines
to help understand one’s Complex System and choose the most adequate model to simulate it.
Simulation consists of mimicking the operation of a
real system in order to understand its behaviour. The
more complicated a system, the more difficult it is to
simulate. And such is the case of Complex Systems
(CSs) that contain a large number of elements with
nonlinear behaviours (Obaidat and Papadimitriou,
2003; Lam, 1998). This study presents an overview
of the CS theories and compares the methods used to
model them. Also, we propose a simple guide that
helps in choosing the appropriate model to describe a
CS in any domain.
The paper is structured as follows. In Section 2,
we explain the main behavioural characteristics in a
CS and we compare its main theories. In Section 3,
we compare the approaches and methods used for
modelling CSs. Then, we propose a simple guide for
selecting the method that fits the CS to model.
Finally, we conclude in Section 4.
The concept of holism considers the system as a
whole in order to study its behaviour. The concept
“the whole is greater than the sum of its parts”, stated
by the Chinese philosopher Confucius, is the heart of
the definition of complexity science that refers to the
study of CSs. A CS is a set of a large number of
interconnected elements that interact with each other
and with the environment in a nonlinear way. These
elements, called agents, are “active, persistent
components that perceive, reason, act, and
communicate” (Huhns and Singh, 1998). The
behaviour within CSs is nonlinear, non-deterministic
and unpredictable. In fact, a CS is guided by a
decentralized complex decision-making process, and
the complexity is generated by the cooperation of
many entities that use their own local rules in order to
evolve and interact through a network of feedback
loops (Lam, 1998; Nicolet, 2010).
2.1 Behavioural Characteristics
A system can be labelled as complex if it expresses a
subset of the following behaviours:
Emergence: is the unexpected production of
new structures, behaviours or patterns, e.g. the V-
shape of a flying flock of birds. Such production
was not programmed beforehand. It rather results
from the continuous interactions. It can be detected
and interpreted by the entities (strong emergence),
or by an external observer (weak emergence)
(Elsner et al., 2015; Lichtenstein, 2014).
Multi-level Structure: CSs enclose a
relationship between the macro level and the micro
Aziza, R., Borgi, A., Zgaya, H. and Guinhouya, B.
Simulating Complex Systems - Complex System Theories, Their Behavioural Characteristics and Their Simulation.
DOI: 10.5220/0005684602980305
In Proceedings of the 8th International Conference on Agents and Artificial Intelligence (ICAART 2016) - Volume 2, pages 298-305
ISBN: 978-989-758-172-4
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
levels. This results from the emergence that can
only be detected at levels higher than the agents. In
addition, CSs can have multiple spatial and
temporal scales (Elsner et al., 2015; Lichtenstein,
2014; Mittal, 2013; Nicolet, 2010).
Distributed Decision-making: In a CS, the
highest level of the hierarchy does not manage and
guide the system. Instead, all actors contribute
through their micro movements. Besides, there is
very little central organization. Thus, the decision-
making mechanism is distributed among the agents
(Nicolet, 2010; Wolf and Holvoet, 2005).
Dynamism and Complicated Interactions: A
CS can be in incremental growth since new entities
can dynamically be created. The interactions
between these entities and the environment are
complex with mechanisms of flow diffusion and
propagation (Mittal, 2013).
Feedback Loops: They occur when an agent
receives stimuli influenced by stimuli that he
issued, and they lead to circular causalities that
complicate the understanding of the system. They
can be convergent or divergent. Convergent loops
attenuate the stimuli and stabilize the system. On
the other hand, divergent loops accentuate the
stimuli and amplify its effects, leading to
exponential change, e.g. the snowball effect or a
spreading fire (Lichtenstein, 2014; Nicolet, 2010).
Adaptability: The environment can limit the
agents’ behaviours, making them adapt to better
achieve their goals. This characteristic shows that
the agents exhibit robustness faced to the
perturbations that occur within their environment
(Johnson, 2007; Wolf and Holvoet, 2005).
Competitiveness and Conflict: Each agent
seeks to satisfy his goals, common or personal.
Thus, agents can be collaborating to reach common
goals, in competition, i.e. expressing a will to live,
or in conflict, e.g. over the use of resources (Mittal,
2013; Rouquier, 2008).
Order: Agents can be simple, intelligent,
ordered, disordered or chaotic. This order is non-
deliberate; it emerges as the agents evolve in their
environments (Wolf and Holvoet, 2005).
2.2 Complex System Theories
“Complexity theory is a set of theoretical and
conceptual tools, not a single theory to be adopted
holistically” (Walby, 2007). Indeed, each theory
stemming from complexity science illustrates real
systems that share some behavioural characteristics.
The main CS theories in the literature are:
Complex Adaptive Systems (CASs): In a CAS,
agents have the ability to acclimatize to changing
environments, making them resilient to
disturbances. The adaptive character emerges from
their will to survive (Mittal, 2013; Thiétart, 2000),
e.g. the ant colonies (Grassé, 1959) and Darwin’s
evolution theory (Darwin, 1977).
Self-organization Theory: The system is
initially in a state of partial or total disorder. A
continuous increase of order allows it to evolve to a
state of order that emerges at a higher level. Such
system maintains its order while the agents adapt
and cope with the changes. It is also constantly
dynamic and responds well to sudden or frequent
changes. For that, it needs to be in a state far from
equilibrium to maintain the order and structure of
the system (Thiétart, 2000), e.g. the study of
patterns such as landscapes (Bolliger et al., 2003).
Stigmergic Systems: Stigmergy is “a series of
repeated stimulus–response cycles” (Lewis, 2013).
It causes a structure to emerge through indirect
communication. The stigmergic complexity stems
from the fact that people interact through the
changes they make in their neighbourhood, which
impacts the others who respond to these changes in
turn (Doyle and Marsh, 2013; Grassé, 1959), e.g.
the dynamics of ant colonies (Grassé, 1959). It is
often considered as a special case of CASs or self-
Coevolution Theory: Coevolution is “the
process of reciprocal adaptation and counter-
adaptation between ecologically interacting
species” (Brockhurst and Koskella, 2013). It
happens when two systems are about to change,
with feedbacks between the components that
influence them, e.g. the coevolution of plants and
viruses (Fraile and García-Arenal, 2010).
Chaos Theory: In chaotic systems, small
changes can lead to very different behaviours,
which make the system exponentially unstable and
unpredictable in the medium and long terms. Unlike
systems capable of emerging order, chaotic systems
have hazardous dynamics (Elsner et al., 2015), e.g.
the butterfly effect (Lorenz, 1963).
Critical Self-organization: happens when the
size of an event is inversely proportional to its
frequency, leading to abrupt system transitions. In
fact, the system starts to evolve steadily until it gets
to the point where small events have repercussions
on the macro level (Thiétart, 2000), e.g. the sand
pile model (Christensen et al., 1991).
Simulating Complex Systems - Complex System Theories, Their Behavioural Characteristics and Their Simulation
Table 1: Comparing the main Complex System theories based on their common behavioural characteristics.
Complex System theories
CAS Self-organization Coevolution Theory of chaos
Emergence key key key key key
yes yes yes yes yes
yes yes yes yes yes
Dynamism and
yes key yes
(random flow
key (micro forces
have global
Feedback loops yes yes key in some cases yes
Adaptability key key key in some cases in some cases
Order yes
key (increase in
no (increase in
Competitiveness in some cases in some cases in some cases in some cases in some cases
The system is in
a poised state
between simple
order and chaos
The system is far
from equilibrium
and changes
Considers other
and hazard
Abrupt transitions
and the event’s
size is inversely
proportional to its
Agents are quite resilient to disturbances
key: important behaviour, yes: expressed behaviour, no: behaviour not expressed, in some cases: the Complex Systems
of this theory may express this behaviour
2.3 A Comparison between Complex
System Theories
The synthesis of our readings on CSs allows us to
establish a summary of the main behavioural
characteristics of different CS theories in Table 1.
Simulation is the imitation over time of the operation
of a real world system or process. It allows the
conduct of virtual experiments where different
scenarios can be tested and predictions could be made
for better decision-making. Moreover, it obviates the
temporal dimension by allowing the simulation of
long periods in a matter of seconds. And it helps avoid
the costs and effects of these tests on reality. The
literature proposes two main approaches for
modelling CSs: the analytical and the systemic
approach (Müller, 2013; Chen et al., 2012).
3.1 The Analytical Approach
This approach is often used for modelling simple
deterministic systems. It requires a prior and
(assumed) complete understanding of the domain
because it needs detailed programming of the
behaviours (Krichewsky, 2008). It works by breaking
down the system into sub-systems. The addition of
the modelling of each part is considered to be the
overall system model. It is therefore based on the
principle of isolating the system’s elements, and
allows the modelling of a small number of linear
interactions. This approach includes:
Differential Equations: This method is well
suited to describe homogeneous populations in
homogeneous environments when continuous
variables are appropriate to represent the whole
population as well as the state of each individual.
However, it is of limited use if the heterogeneity of
the entities is too high to be reasonably described
with variables (Breckling, 2002), e.g. equation
based modelling of obesity (Thomas et al., 2014).
Stochastic Processes: In the study of some CSs,
hazard can be important in determining the outcome
of the system. The difficulty of modelling the
“interplay of chance and necessity” (Lam, 1998)
can be caused by the lack of data in the studied field,
the inability to recreate the events, and the absence
of a realistic mathematical model representing these
CSs. Stochastic systems are widely used to
represent hazardous dynamics, e.g. the stochastic
description of human feelings (Carbonaro and
Giordano, 2005).
Limits of the analytical methods in modelling
CSs: Differential equations and stochastic processes
can be combined, and other techniques of Artificial
Intelligence can also be used at different levels, such
as Fuzzy Logics for representing vague and imprecise
ICAART 2016 - 8th International Conference on Agents and Artificial Intelligence
knowledge, Multimodal Logics for representing
symbolic data, and neural networks for optimizing
complex tasks. However, these methods fail to model
the nonlinearity and unpredictability of CSs. In fact,
they describe relationships as global parameters, and
do not explicitly account for the fact that these
relationships result from the interlocking behaviours
of individuals. Thus, analytical methods reduce the
overall system into a set of parts, causing a loss of
relationships that could emerge from their
coexistence. They are useful in modelling systems
that have deterministic dynamics, predictable
behaviours and centralized decision-making
(Krichewsky, 2008; Thiétart, 2000).
3.2 The Systemic Approach
This approach overcomes the limits of the analytical
one. It considers the system as a whole and focuses
on the dynamic relationships between its components,
rather than the characteristics of each component
considered separately. The elements’ behaviour is
guided by objectives, which promotes complex
behaviours, namely, emergence (Müller, 2013). The
systemic models can be categorized as traditional
models or constructivist models.
3.2.1 Traditional Systemic Models
Examples of traditional systemic models:
Rule based Systems: they are based on an
inference engine that uses uniform rules given by
experts. They are used when: the interacting
variables are not numerous, the system processes
are understood and the knowledge expressed by the
experts is considered complete (Chen et al., 2008).
Despite its limitations, this method has been used
for CSs, for example, rule-based simulation of
biochemical systems (Harris et al., 2009).
Artificial Neural Networks: they imitate the
way human brains work. They are composed of a
set of interconnected nodes, and use nonlinear
calculations that fit complex and multivariable data
(Chen et al., 2008).
3.2.2 Constructivist Models
Constructivist models keep the link between the
overall system behaviour and the behaviour of local
elements. They are used to represent different level
entities, e.g. molecule, cell, person, and group, and
the interactions between them (Müller, 2013). They
can be classified into two main categories: Individual-
Based Models and Multi-Agent Systems. Individual-based Models (IBMs)
The most known IBMs are:
Synergistic Modelling: It is based on a
stochastic description of the individual decision-
making processes. The link between the individual
level and the macrostructure level is modelled with
continuous differential equations that express the
probability of a given configuration, e.g. modelling
dialogues between people (Fusaroli et al., 2013).
Microsimulation: It expresses the decision-
making processes of an individual using probability
(Koch, 2015). An agent behaves and interacts based
on stochastic parameters, and each decision takes
into account the choice made by the individual at an
earlier time. This mechanism allows individuals to
have different behaviours.
Limits of synergistic models and
microsimulation: Individual decisions in synergistic
models are explained by macroscopic factors and not
intra-individual features. Also, the behaviours can
only be homogeneous. Besides that, in both
synergistic models and microsimulation, individuals
are very independent; decisions are not influenced by
social nor spatial factors. In these models, space is not
taken into account, unless modelled as a global
parameter. In addition, these models do not consider
interactions between individuals and their
environment nor the spatial influence of their actions.
Thus, if a macrostructure emerges from the sum of
individual actions, it cannot be retroactive back to the
individuals (Koch, 2015; Laperriere, 2004).
Cellular Automaton (CA): A CA is a spatial
model that is discrete in space and time. It models
homogeneous populations residing in a physical
environment. It is composed of identical cells in a
regular grid. All cells are updated every unit of time,
and their states are determined by the same set of
rules. A state depends only on the cell’s current state
and its immediate neighbours’ states. Complex
dynamics and emerging properties can result from
this monotonous and simple update (Qu et al., 2011;
Kari, 2005), e.g. simulating people’s movement
(Sarmady et al., 2011).
Limits of CA: A CA automatically provides a
spatial dimension. Yet it treats the distances between
adjacent agents as uniform, and private relations
between distant cells are not allowed. Thus, social
relations are limited to spatial proximity. A CA also
has a problem with border conditions. In fact, since a
cell’s state depends on its neighbours, the borders
may face some miscalculations. In order to avoid this
problem, we can model a large CA grid that will
dispel border errors. But this solution reduces the
performances because all cells are recalculated at
every step, even the vacant ones (Chen et al., 2008).
Simulating Complex Systems - Complex System Theories, Their Behavioural Characteristics and Their Simulation
301 Multi-Agent Systems (MASs)
A MAS is composed of agents that evolve within a
social network and a physical environment. These
agents are heterogeneous, dynamic and independent
(Siebers et al., 2010). They can represent different
levels: genes, cells, organs, individuals, and
organizations. Each agent influences others, changes
its state or thoughts, and modifies its environment. A
MAS can have spatial components that are
represented via spatial agents or as part of the
system’s configuration. Agents can also have agency;
they behave in a way that satisfies at best their
personal goals. Such behaviour can be unconscious
and deterministic. In such case, the agents are
reactive. It can also rely on human-like thinking
mechanisms; such agents are cognitive. These latter
perceive, reason and execute. Their internal state can
be expressed via beliefs, desires, preferences,
intentions, emotions, etc. (Bagdasaryan, 2011; Qu et
al., 2011; Frantz, 2012).
The MAS paradigm is very useful in modelling
social systems, because it can take into account the
human behaviour, the complex reasoning, and the
psychological factors (Chen et al., 2008). As for
classifying MASs, Rouquier (2008) claims that they
are not part of CS models. Among other reasons, he
states the fact that an agent can change his behaviour,
yet according to him, behavioural rules in CSs are
simple and unchangeable. On the other hand, many
other researchers (Mittal, 2013; Doyle and Marsh,
2013) consider MAS to be positively suited for
modelling CSs. We stand by the latter opinion, and
we consider that the system’s complexity can be
described by simple entities, but can also result from
an intrinsic complex behaviour, which goes in tandem
with the multi-level hierarchy of CSs. E.g. the MAS
of marketing research (Negahban and Yilmaz, 2014).
Limits of MASs: MASs help cut off some limits of
IBMs. Nevertheless, while modelling a MAS, the
designer needs to find a balance between modelling
all identified factors and keeping it simple. Indeed,
simplifying might result in eliminating some micro-
factors that may cause emergence later on. So the
objective is to keep the model understandable and to
limit the unnecessary complexity without harming
emerging effects (Bonabeau, 2002; Axelrod, 1997).
Besides that, MASs generally require a lot of
modelling time and computing resources because
they need a deep understanding of all actors in the
system, e.g. reasoning mechanisms, conflicts, and
resources. In addition, since it is often used for
simulating social and human behaviours, MASs
require significant technical and interdisciplinary
competences (Frantz, 2012; Bonabeau, 2002).
3.3 Comparing the Methods Used to
Model Complex Systems
In this section, we draw a comparison between the
analytical and the systemic approaches. Then we
compare the different constructivist methods.
3.3.1 Analytical Vs. Systemic
The analytical and the systemic approaches differ in
principle, see Table 2. The first one only takes into
account the elements’ state and behaviour, while the
second focuses more on the interactions between the
elements and with the environment (de Rosnay,
1975). An emergent phenomenon cannot be studied
using a reductionist paradigm as the latter has its
limitations especially in capturing the nonlinear
behaviours (Lichtenstein, 2014). Nevertheless, it is
still very useful in modelling CSs. In fact, in some
cases, it can prove to be more suitable as a choice for
describing a given CS. For example, if a system has
processes that can be considered as reversible, its
dynamics are linear and it contains quite simple
interactions, then a deterministic analytical approach
is appealing and probably more representative of the
studied aspect of the system, e.g. the modelling for
predicting obesity prevalence trends (Thomas et al.,
2014). Such choice should greatly take into account
the specific aspect that the designer aims to
understand, and not all the phenomena that occur
within the CS.
Table 2: Analytical approach vs. systemic approach
(Nicolet, 2010; de Rosnay, 1975).
Analytical approach Systemic approach
Reductionism Holism
Predictable, deterministic Unpredictable behaviour
Elements isolated from
their environment
Element are not isolated
from their environment
Linear, simple
Nonlinear complex
Focuses on the elements
Focuses on the
dynamics of relations
Guided by details Guided by goals
The temporal dimension
is considered reversible
The temporal dimension
is acknowledged as
Validation: experimental
evidence based on a
Validation: comparison
with reality
ICAART 2016 - 8th International Conference on Agents and Artificial Intelligence
Furthermore, the two approaches can be
combined. For instance, we can have a MAS with
stochastic dynamics, e.g. the MAS for studying
diseases (Snijders et al., 2010). The choice of a
combined model depends on the modelled processes
and the researcher’s preferences (Bagdasaryan,
2011). In the following paragraph, we go further by
comparing systemic constructivist models.
3.3.2 Comparing the Constructivist
Constructivist models keep a link between the global
behaviour and the local behaviours of the elements.
They allow explaining the overall behaviour based on
individual behaviours, and they are very appropriate
for modelling social and ecosystems (Müller, 2013).
In Table 3, we compare the constructivist models.
This comparison is based on a non-exhaustive set of
dimensions, system behavioural characteristics, and
agent behaviours.
3.4 How to Select a Method for
Modelling a Complex System?
We believe the method that models a CS should
be carefully chosen on a case-by-case basis. This
choice is important and has great influence on the
outcome of the model. In fact, it mainly depends on
the system’s characteristics, the available resources,
the designer’s abilities, and our understanding of the
system’s dynamics. In this section, we propose a
simple guide to help designers understand their CS’s
main behavioural characteristics, in order to choose
the appropriate model for it. This guide, see Figure 1,
can be applied in any field of study since all the steps
are independent of the application context.
The designer first selects a CS theory that best
describes the CS to model. For that, he/she relies on
their knowledge of the system, their study goal, and
the comparison in Table 1. Then, the user chooses the
approach to follow based on the goal of the study and
the comparison depicted in Table 2. If the chosen
approach is analytical, the need to model hazard
within the system allows the designer to pick either
stochastic processes or differential equations.
Table 3: Comparing the systemic constructivist models.
Spatial dimension
no (modelled
as a global
no (modelled
as a global
Social dimension no no
yes (adjacent
Cognitive dimension no no no yes
Difficulty of designing the system (e.g. resources,
time, and call for interdisciplinary skills)
medium medium medium difficult
System behavioural characteristics
Emergence yes yes yes yes
Local (agent agent) yes yes yes yes
Global (global emergence agent) no no yes yes
Open system yes yes
no (errors at
the borders)
Agent’s behaviour
Autonomy regarding the environment yes yes no yes
Interaction between individuals and their
no no yes yes
Heterogeneous agents no yes no yes
Dynamic inter-agent relations no no no yes
Interaction between distant agents no no no yes
involved in
Spatial factors no no yes yes
Social factors no no
yes (adjacent
Intra-individual factors (other than
no yes yes yes
Cognitive factors no no no yes
Simulating Complex Systems - Complex System Theories, Their Behavioural Characteristics and Their Simulation
If the approach is systemic, the user decides if it
is necessary to keep a link between the macro and
micro levels of his/her model; this is important in case
we want to model emergent phenomena because, as
we said earlier, emergence can be detected on levels
higher than the agents themselves, but it is caused by
the agents’ micro dynamics.
Figure 1: How to choose a method to simulate a CS in any
field of study. (a) Table 1, (b) Table 2, (c) Table 3.
Therefore, a link between the micro and macro
levels is crucial for modelling emergence. If no such
phenomena need to be modelled, the designer should
opt for one of the traditional systemic models.
Otherwise, he/she should choose between the
constructivist models.
In fact, the proposed guide facilitates the task of
designing CSs. Nevertheless, it does not take into
consideration combining several models, e.g.
constructivist/traditional systemic, constructivist
/analytical, traditional systemic/analytical, and
constructivist/constructivist. Thus, it should be
extended to allow more flexible choices, and also
propose the supporting tools for each choice.
We would also like to point out that identifying
the CS theory to adopt could be quite difficult. In fact,
more than one theory may seem appropriate because
they share some behavioural characteristics e.g. CAS
and self-organizing systems, or evolution and
coevolution theories. In such cases, one should limit
the suitable theories, and make the final decision after
a deeper needs analysis of the studied aspects of the
CS. In some cases, both the analytical and the
systemic approaches can be suitable candidates. For
instance, in the study of obesity, the literature
proposes equation based models (Thomas et al.,
2014) and MASs (Aziza et al., 2014). Besides that, a
further study should be made in order to apply this
guide on different contexts of different domains.
In this article, we presented an overview of modelling
CS. We first took a step back, studied the main
behavioral characteristics in complexity science, and
compared its main theories, namely, CAS, chaos
theory, and coevolution theory. We described and
compared the different approaches and models used
for simulating CSs. Then, we proposed and discussed
a simple tool that lists some guidelines to help
understand one’s complex context and choose the
most adequate model to simulate it.
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