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.

1 INTRODUCTION

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.

2 COMPLEX SYSTEMS

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

298

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

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-

organization.

 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).

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Table 1: Comparing the main Complex System theories based on their common behavioural characteristics.

Behavioural

characteristics

Complex System theories

CAS Self-organization Coevolution Theory of chaos

Catastrophic

complexity

Emergence key key key key key

Multi-level

structure

yes yes yes yes yes

Distributed

decision

yes yes yes yes yes

Dynamism and

complicated

interactions

yes key yes

key

(random flow

propagation)

key (micro forces

have global

effects)

Feedback loops yes yes key in some cases yes

Adaptability key key key in some cases in some cases

Order yes

key (increase in

order)

yes

no (increase in

disorder)

key

Competitiveness in some cases in some cases in some cases in some cases in some cases

Other

The system is in

a poised state

between simple

order and chaos

The system is far

from equilibrium

and changes

frequently

Considers other

agents’

simultaneous

changes

Exponential

instability,

unpredictability

and hazard

Abrupt transitions

and the event’s

size is inversely

proportional to its

frequency

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.

3 SIMULATING COMPLEX

SYSTEMS

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

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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.

3.2.2.1 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).

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3.2.2.2 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

interactions

Nonlinear complex

interactions

Focuses on the elements’

characteristics

Focuses on the

dynamics of relations

Guided by details Guided by goals

The temporal dimension

is considered reversible

The temporal dimension

is acknowledged as

irreversible

Validation: experimental

evidence based on a

theory

Validation: comparison

with reality

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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

Models

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.

Models

Synergistic

modelling

Microsimulati

Cellular

Automata

Multi-Agent

Systems

Dimensions

Spatial dimension

no (modelled

as a global

parameter)

no (modelled

as a global

parameter)

yes

(mandatory)

yes

Social dimension no no

yes (adjacent

neighbours)

yes

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

Feedback

loops

Local (agent ↔ agent) yes yes yes yes

Global (global emergence → agent) no no yes yes

Open system yes yes

no (errors at

the borders)

yes

Agent’s behaviour

Autonomy regarding the environment yes yes no yes

Interaction between individuals and their

environment

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

Factors

involved in

agents’

decision-

making

Spatial factors no no yes yes

Social factors no no

yes (adjacent

neighbours)

yes

Intra-individual factors (other than

cognitive)

no yes yes yes

Cognitive factors no no no yes

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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.

4 CONCLUSIONS

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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