Mayara Segatto, Leonardo Augusto Amaral Terra, Dante Pinheiro Martinelli
Universidade de São Paulo, BRA
Complexity is usually pointed out as a characteristic inherent to the various dynamics of daily life in the global context, which requires an approach from a coherent epistemological foundation. This article seeks to list the essential concepts and principles related to the theory of complexity, since there is not, in literature, a work that gathers such concepts. This work makes a conceptual review in two stages. The first one is based on the non-structured review of the literature. The second stage consists of a structured bibliographic research intended to find updates, detailing and criticisms to the central concepts of this approach, seeking the state of the art in the topic. As a result, the essential concepts of the complexity theory are defined, configuring an academic contribution by gathering such concepts and suggesting an approach for analysis and treatment of complex phenomena.
Key words: 1. Complexity; 2. Concepts; 3. Systems.
Several researchers point out complexity as characteristic of everyday life (Bertalanffy, 1972) marked by challenges (Morin, 2010), crises (Capra, 1983), uncertainty (Prigogine, 1997), confusion and drastic changes that emphasize the interconnection between the seemingly isolated events or trends (Toffler, 1981). Dealing with this context requires increasingly new ways of thinking.
The change in paradigm, reflected in the emergence of new scientific approaches, is frequently justified by the need to deal with the complexity and transdisciplinarity of contemporary problems. When a paradigm is understood as a fundamental assumption, as an accepted model or standard (Kuhn, 1996), there is a need to look for alternatives to reductionism, looking for new assumptions on which grounds thought would be possible.
Reductionist fragmentary knowledge must be overcome, since reality is distorted when reduced to the perspective of a single discipline, making of it an insufficient approach to dealing with complex problems (Capra, 1983; Morin, 2010, 2011; Toffler, 1981; Terra & Passador, 2015, 2018). The reductionist approach is insufficient to deal with the totality of the problems, gradually atrophying the possibilities of understanding and reflection (Morin, 2010). Axley and Macmahon (2006) argue that the Cartesian-Newtonian paradigm possibly reached its limits of effectiveness in the face of the dynamics and uncertainty of the world.
There is a need for a globalizing vision of reality. According to Morin (2010), the reform of thinking must generate a thought of the context and of the complex. It became necessary to find ways to understand and evaluate growing patterns of conflict, unpredictability, flow, dynamic equilibrium, breakdowns, discoveries and transnational relations (Dennis, 2007). In this sense, complexity criticizes the division of knowledge into disciplines, because in every piece of the whole there is another piece of the unknown.
Complexity is an ascending paradigm, configuring a change in mentality (Goulielmos, 2005). In allowing a better understanding of the context, the theory of complexity provides concepts that can assist in management and decision-making in different areas. It not only implies that global processes are sustained by multiple interconnections, but also that events, both local and global, do not exist in an isolated way, but produce effects by means of non-linear interrelations (Dennis, 2007).
Considering the abovementioned and the environment of complications, uncertainty and non-linearity, using emerging paradigms as the basis for the studies of phenomena and seeking them to understand them seems appropriate. Among the reasons for which one seeks to describe and understand complexity as precisely and as well as possible is the desire to reduce and to increase complexity. That means, seeking to build higher levels of complexity because they are the most efficient means of action and, at the same time, trying to reduce it with the aim of minimizing unwanted effects and being able to cope with increasing levels of complexity (Nowotny, 2005). Therefore, it is possible that the complexity paradigm set up a coherent alternative to understand the uncertainty of phenomena and describe them.
As the basic concepts of complexity theory are not strictly defined in a specific text (Bloch, 2005), one of the great difficulties to be overcome in this transdisciplinary process is to avoid the distortion of conceptual definitions, common when these are transposed between disciplines, fragmented by Cartesian thinking. Aiming to help minimize this problem, this study seeks to fill this gap in literature, gathering and defining the basic principles of this theoretical approach, including current perspectives in the field. Thus, this compilation aims to facilitate for new researchers, to overcome the initial difficulties to familiarize yourself with this conceptual basis, through a structured synthesis of important concepts to be considered in the study of complexity. Based on the conceptual framework presented, it is expected to reduce the inappropriate use of terms or the distortion in their basic definitions, which are frequent when they are transposed between distinct areas of knowledge.
The next section presents the research phases adopted in this article. Subsequently, the essential concepts of the complexity theory are detailed, and an approach is proposed for the treatment of complex phenomena. Finally, the last section consists of the final considerations, presenting the contribution, limitations and suggestions for future studies.
The gathering of evidence for this study followed two distinct phases. In a first moment, literature on the theory of complexity was reviewed. In a second moment, the phase of bibliographic research was conducted, with the aim of checking the state of the art literature on the subject, allowing the analysis of the basic concepts and contemporary studies in search of evolution, changes, criticism or of the emergence of new concepts in this area.
Based on the literature review conducted previously, some terms and concepts, considered essential for the theory of complexity, were highlighted from the reading of consecrated authors and classical works in this area. The results of the terms related to the main definitions of complexity found in this preliminary study, are shown in Table 1.
| Concept and Authors | Definition |
|---|---|
| Attractors (Agar, 1999; Bloch, 2005; Longa, 2004; Manson, 2001; Puddifoot, 2000; Rickles, Hawe & Shiell, 2007) | The behavior of nonlinear dynamic systems may, in certain conditions, possess an attractor, which is an invariant group to which nearby orbits converge after some time. |
| Self-organization (Morin, 2010; Murray, 1998; Rickles, Hawe and Shiell, 2007) | Happens when systems are spontaneously organized, without external influence. |
| Chaos or sensitive dependence to initial conditions (Fiedler-Ferrara and Prado, 1994) | Chaotic behavior results from the nonlinearities present in the system, exponentially magnifying small differences in the initial conditions, generating out-of-proportion nonlinear consequences to the evolution of the system. |
| Emergency (Ashby, 1970; Morin, 2010) | Concerns the specific properties of each hierarchical level, i.e., they emerge from each one of them and make sense only in the level of abstraction in which they appear, being unpredictable from the knowledge of the parties and its couplings, i.e., properties presented as a whole, but that could not be found in any of the parts, separately. |
| Stability or dynamic equilibrium (Fiedler-Ferrara & Prado, 1994) | The systems operate within the limits of chaos, or in the edge of chaos, which would be where the system reaches a state of dynamic equilibrium around an attractor, between order and chaos, or stability and change. |
| Identity (Beer, 1985, 1994a, 1994b) | The system has an existence and an identity of its own, which defines it. The aim or purpose of the system reveals aspects of its identity. |
| Nonlinearity (Bertalanffy, 1972) | A nonlinear system is one which outputs cannot be forecast from the initial conditions, along a straight or stable trajectory, i.e., a system which response is not proportional to the stimulus applied, and which allows multiple solutions. |
| Fractal Patterns (Gleick, 1987; Morin, 2010, 2011) | The lowest point of the image contains almost all the information of the object represented. |
| Recursion (Beer, 1985; Morin, 2010, 2011) | Generating circuit in which the outcomes and effects are the producers and causers of what they produce, in a self-constituting, self-organizing and self-producing cycle. The system exists at several scales (or recursion levels) and several recursive dimensions, i.e., it belongs to several systems’ chains. |
| Retroactivity or feedback (Morin, 2010) | Positive or negative feedback, the multiple retroactions of a system are inter-related and suffer the effects of uncertainty. |
| Dynamic and Irreversible System (Bloch, 2005; Capra, 1983) | Irreversibility is determined by temporal insertion, i.e., any ‘after’ is different from ‘before’. |
| Variety (Ashby, 1970; Beer, 1985, 1994a) | Variety counts the number of possible states of a system. |
| Viability (Beer, 1985; Capra, 1983) | A system is viable if it can survive autonomously in a particular type of environment. |
Table 1: Basic concepts of the theory of complexity resulting from the review of literature. Source: organized by the authors.
From these terms listed in Table 1, a search was carried out to find basic concepts in data bases were previously defined, with the purpose of finding updates, detailing and criticism to the central notions of complexity. Thus, this stage allowed including the recent production in literature on the subject, adding to the classical works consulted. The first definition of the search terms is presented in table 2.
| Terms of Search |
| Chaos |
| Dynamic equilibrium |
| Dynamic stability |
| Dynamic system |
| Emergence |
| Feedback |
| Fractal |
| Identity |
| Nonlinearity |
| Recursion |
| Self-organization |
| Sensitive dependence |
| Sensitivity to initial conditions |
| Strange attractors |
| Variety |
| Viability |
Table 2: Initial proposal of the terms of search for bibliographic search. Source: organized by the authors.
As some terms presented a common area of meaning, they were respectively reduced to a more general term, as an attempt to minimize duplicate results in searches. Table 3 shows the terms used for bibliographic searches.
| Terms of Search | Final Terms of Search |
|---|---|
| Chaos | Chaos |
| Dynamic equilibrium | Dynamic |
| Dynamic stability | |
| Dynamic system | |
| Emergence | Emergence |
| Feedback | Feedback |
| Fractal | Fractal |
| Identity | Identity |
| Nonlinearity | Nonlinearity |
| Recursion | Recursion |
| Self-organization | Self-organization |
| Sensitive dependence | Sensitivity |
| Sensitivity to initial conditions | |
| Strange attractors | Attractor |
| Variety | Variety |
| Viability | Viability |
Table 3: Terms of search for bibliographic search. Source: organized by the authors.
The searches were performed from these terms, combined with the "complexity theory" or "complexity science". These filter terms were chosen from the works used in the literature review mentioned in the approach. The use of the term "complexity" alone generated a very large quantity of results not necessarily related to the theory of complexity; instead, its colloquial meaning was used, representing something "complicated". Thus, the choice of the compound terms is justified.
The databases used were the ISI Web of Knowledge and Scopus. Studies published in academic journals were chosen in the selection, since they are subjected to the process of peer review, being evaluated in detail. A restriction in the time interval was not established, considering all the years available in its database. Therefore, two search filters (F) were used during the searches:
F1 - Articles published in academic periodicals indexed in the databases used for the search; and
F2 - Studies containing one of the combinations of the search terms previously defined in the fields: "Article Title, Abstract, Keywords", in the SCOPUS; and "Topic", in the ISI Web of Knowledge, which covers the same fields used in the SCOPUS - article title, abstract, keywords.
The result of the preliminary search with the application of search filters is shown in table 4.
| Search Terms | ISI Web of Knowledge | Scopus | Total |
|---|---|---|---|
| Attractor | 28 | 38 | 66 |
| Chaos | 141 | 180 | 321 |
| Dynamic | 289 | 194 | 483 |
| Emergence | 102 | 153 | 255 |
| Feedback | 49 | 63 | 112 |
| Fractal | 27 | 47 | 74 |
| Identity | 29 | 40 | 69 |
| Nonlinearity | 13 | 23 | 36 |
| Recursion | 19 | 22 | 41 |
| Self-organization | 79 | 109 | 188 |
| Sensitivity | 27 | 25 | 52 |
| Variety | 64 | 72 | 136 |
| Viability | 7 | 8 | 15 |
| Total | 874 | 974 | 1848 |
Table 4: Results of preliminary search in the databases for each term. Source: organized by the authors.
Two exclusion criteria (EC) were also followed:
EC 1 - Studies in duplicity (repeated) in the databases and between them;
EC 2 - Studies in languages other than Portuguese, English or Spanish.
After the phase of search in databases is concluded and the EC is applied (excluded from 880 articles), the reading of the title, abstract and keywords of each article was carried out (968 articles in total), selecting the studies by means of two inclusion criteria (IC):
IC 1 - Studies with theoretical contribution covering elementary definitions and concepts of the complexity theory;
IC 2 - Studies with theoretical contribution containing criticism to the theory of complexity and their definitions and concepts.
In cases in which it was not possible to verify the inclusion criteria by reading the items cited, the reading of the full study (12 articles) was performed. The search resulted in the selection of 89 articles for analysis, represented in table 5.
| Data Base | Selected by F | Excluded by EC | Selected by IC |
|---|---|---|---|
| ISI Web of Knowledge | 874 | 435 | 46 |
| Scopus | 974 | 445 | 43 |
| Total | 1848 | 880 | 89 |
Table 5: Studies selected for analysis. Source: organized by the authors.
The analysis of the articles was initiated from their selection, consisting of a detailed procedure to search the following information:
Still during this phase of the research, after careful analysis of each Article, 55 works were discarded because they did not contribute significantly to this research, summing up 34 articles used, listed in table 6. These articles originated a new cycle of research, based on their references and concepts, leading to the conceptual frameworks built at the end of this article.
| Authorship | Title | Year | Source |
|---|---|---|---|
| Abraham, R. H. | The genesis of complexity | 2011 | World futures: The Journal of Global Education |
| Agar, M. | Complexity theory: an exploration and overview based on John Holland's work | 1999 | Field Methods |
| Alhadeff-Jones, M. | Three generations of complexity theories: nuances and ambiguities | 2008 | Educational Philosophy and Theory |
| Barabási, A.-L. | The architecture of complexity | 2007 | IEEE Control Systems Magazine |
| Bloch, D. P. | Complexity, chaos, and nonlinear dynamics: a new perspective on career development theory | 2005 | The Career Development Quarterly |
| Bokeno, M. | Complexity: an alternative paradigm for teamwork development | 2008 | Development and Learning Organizations |
| Bousquet, A.; Curtis, S. | Beyond models and metaphors: complexity theory, systems thinking and international relations | 2011 | Cambridge Review of International Affairs |
| Burnes, B. | Complexity theories and organizational change | 2005 | International Journal of Management Reviews |
| Dennis, K. | Time in the age of complexity | 2007 | Time & Society |
| Goulielmos, A. M. | Complexity theory: a science where historical accidents matter | 2005 | Disaster Prevention and Management |
| Horn, J. | Human Research and Complexity Theory | 2008 | Educational Philosophy and Theory |
| Howard, A. | Paradexity: the convergence of paradox and complexity | 2010 | Journal of Management Development |
| Johnson, J. | The future of the social sciences and humanities in the science of complex systems | 2010 | Innovation: The European Journal of Social Science Research |
| Katopes, P. | Resisting chaos: the power of the humanities as a problem-solving system | 2011 | On the Horizon |
| Klijn, E.-H. | Complexity theory and public administration: what's new? | 2008 | Public Management Review |
| Kogetsidis, H. | Systems approaches for organisational analysis | 2011 | International Journal of Organizational Analysis |
| Larsen-Freeman, D. | Complex, dynamic systems: a new transdisciplinary theme for applied linguistics? | 2012 | Language Teaching |
| Lindsay, V. J. | The development of international industry clusters: a complexity theory approach | 2005 | Journal of International Entrepreneurship |
| Longa, V. M. | A nonlinear approach to translation | 2004 | Target |
| Manson, S. M. | Simplifying complexity: a review of complexity theory | 2001 | Geoforum |
| Manson, M. | What is complexity theory and what are its implications for educational change? | 2008 | Educational Philosophy and Theory |
| Mathews, K. M.; White, M. C.; Long, R. G. | Why study the complexity sciences in the social sciences? | 1999 | Human Relations |
| Miguélez, M. M. | Paradigmas emergentes y ciencias de la complejidad | 2011 | Opción |
| Mikulecky, D. C. | The emergence of complexity: science coming of age or science growing old? | 2001 | Computers and Chemistry |
| Mowles, C. | Post-foundational development management - power, politics and complexity | 2010a | Public Administration and Development |
| Mowles, C. | Successful or not? Evidence, emergence, and development management | 2010b | Development in Practice |
| Murray, P. J. | Complexity theory and the fifth discipline | 1998 | Systemic Practice and Action Research |
| Nowotny, H. | The increase of complexity and its reduction: emergent interfaces between the natural sciences, humanities and social sciences | 2005 | Theory, Culture & Society |
| Phelan, S. E. | A note on the correspondence between complexity and systems theory | 1999 | Systemic Practice and Action Research |
| Pina e Cunha, M.; Rego, A. | Complexity, simplicity, simplexity | 2010 | European Management Journal |
| Poser, H. | Theories of complexity and their problems | 2007 | Frontiers of Philosophy in China |
| Puddifoot, J. E. | Some problems and possibilities in the study of dynamical social processes | 2000 | Journal for the Theory of Social Behaviour |
| Rickles, D.; Hawe, P.; Shiell, A. | A simple guide to chaos and complexity | 2007 | Journal of Epidemiology & Community Health |
| Sanger, M.; Giddings, M. M. | A simple approach to complexity theory | 2012 | Journal of Social Work Education |
| Terra, L. A. A; Passador, J. L. | A Phenomenological Approach to the Study of Social Systems | 2015 | Systemic Practice and Action Research |
| Terra, L. A. A; Passador, J. L. | Strategic Thinking in The Context of Complexity | 2018 | Systems Research and Behavioral Science |
Table 6: Final selection of the articles for updating of the knowledge on the theory of complexity. Source: organized by the authors.
Complexity or complexity theory involves a series of concepts originated from the so-called hard sciences. The systems theory (Abraham, 2011; Bousquet & Curtis, 2011; Capra, 1983; Manson, 2001; Morin, 2011; Terra & Passador, 2015, 2018), cybernetics (Abraham, 2011; Bousquet; Curtis, 2011; Manson, 2001; Morin, 2011), the theory of information (Morin, 2011), the neural approach (Manson, 2001) and the dynamics of systems (Abraham, 2011; Bousquet & Curtis, 2011) are cited as the main theoretical references constituting the bases of complex thinking, although there is no consensus about the chronological order of emergence and development of these approaches.
Based on this, some authors have criticized the reduction to a singular form—complexity theory or science of complexity—claiming this might lead to the neglect of a series of theories (Alhadeff-Jones, 2008; Barabasi, 2007; Burnes, 2005; Klijn, 2008; Manson, 2001; Mathews, White & Long, 1999; Morin, 2011). Thinker Edgar Morin, a prominent name in the study of complexity, proposes a change in the way of thinking (Morin, 2010, 2011), suggesting the construction of a new paradigm. However, the interconnections between those theoretical bases have increased and, possibly, the complex system of ideas has become a larger system (Abraham, 2011; Mathews, White & Long, 1999; Manson, 2001), and now is more like a group of concept tools than a definite theoretical body (Bousquet & Curtis, 2011). For these reasons, this group of concepts will be approached here, despite the criticisms, as complexity or complexity theory, in order to make easier the reference to such conceptual tools.
There is no unanimity in the formulation of the concept of complex system, and it is possible to observe many different definitions (Goulielmos, 2005; Johnson, 2010; Miguelez, 2011; Mikulecky, 2001). Complex Systems are imbalance models, continuously changing through contradictory mechanisms that compete among themselves for effectiveness (Agar, 1999). According to Rickles, Hawe and Shiell (2007), complex systems are compounds build by large quantities of mutually interactive subunits, which repetitive interactions result in a rich collective behavior that feeds back the behavior of individual parties. For Sanger and Giddings (2012) a complex system consists of many subsystems interacting among themselves by means of multiple cycles of non-linear and recursive feedback.
From literature review and bibliographic research, were defined the fundamental concepts of complexity, listed in table 7.
| Concept | Definition | References |
|---|---|---|
| Adaptability | Mutual Adaptation between groups and individuals, both within the group and in relation to the environment. It concerns the ability to learn from experience and change behaviors based on that, absorbing instabilities or noise of external origin. | Bloch, 2005; Bousquet & Curtis, 2011; Kauffman, 1991; Manson, 2001; Murray, 1998; Miguelez, 2011; Varela, Maturana & Uribe, 1974 |
| Attractors | The behavior of nonlinear dynamic systems may, in certain conditions, possess an attractor, which is an invariant group to which nearby orbits converge after some time. Once the system reaches a certain critical level of complexity, the transition phase or bifurcation takes place, changing the attractors of the system. | Bloch, 2005; Kauffman, 1991; Puddifoot, 2000 |
| Self-organization | Happens when the systems organize themselves spontaneously, without external influence. Living beings as self-organizing beings do not cease to self-reproduce and for this reason, depend on energy for maintenance of autonomy. Self-organization is linked to the emergent behavior of complex systems, since the organization of the whole cannot be predicted from the behavior of the parties. | Bloch, 2005; Bokeno, 2008; Bousquet & Curtis, 2011; Kauffman, 1991, Klijn, 2008; Larsen-Freeman , 2012; Lindsay, 2005; Miguelez, 2011; Morin, 2010; Murray, 1998; Prigogine, 1997; Rickles, Hawe & Shiell, 2007; Varela, Maturana & Uribe, 1974 |
| Co-evolution | Refers to the system that does not reach a state of equilibrium, continuously evolving—an evolution that does not imply progress, but simply that the system cannot return to its previous state. There is mutual influence between system and subsystems, forming an evolving network. It describes, thus, the way organisms create their environment and are shaped by it, because of the feedback. | Bousquet & Curtis, 2011; Kauffman, 1991, Kauffman & Johnsen, 1991; Klijn, 2008; Lindsay, 2005; Margulis & Sagan, 1995; Murray, 1998; Rickles, Hawe & Shiell, 2007 |
| Sensitive dependence to initial conditions or chaotic behavior | Chaotic behavior results from the nonlinearities present in the system, exponentially magnifying small differences in the initial conditions, generating out-of-proportion nonlinear consequences to the evolution of the system. In addition, there is the possibility of emergence of random events due to the presence of an attractor. This way, deterministic laws of evolution can lead to chaotic behaviors, even in the absence of external noise or fluctuations. | Bloch, 2005; Larsen-Freeman, 2012; Prigogine, 1997 |
| Emergency | Concerns the specific properties of each hierarchical level, i.e., , they emerge from each one of them and make sense only in the level of abstraction in which they appear, being unpredictable from the knowledge of the parties and its couplings, i.e., properties presented as a whole, but that could not be found in any of the parts, separately. | Agar, 1999; Ashby, 1970; Bloch, 2005; Bokeno, 2008; Bousquet & Curtis, 2011; Kauffman, 1991; Klijn, 2008; Larsen-Freeman, 2012; Long, 2004; Manson, 2001; Mason, 2008; Mikulecky, 2001; Morin, 2010; Murray, 1998 |
| Dynamic Equilibrium | The systems operate within the limits of chaos, or in the edge of chaos, which would be where the system reaches a state of dynamic equilibrium around an attractor, between order and chaos, or stability and change. | Burnes, 2005; Lindsay, 2005; Miguelez, 2011 |
| Unpredictability | Emergency, non-linearity and dependence sensitive to the initial conditions make prediction and control impossible, once changes in a subsystem aimed at changing the whole may not get the expected result, since the other components of the system will change to accommodate the intervention, in addition to other changes in the environment. | Bloch, 2005; Larsen-Freeman, 2012; Poser, 2007 |
| Non-linearity | A nonlinear system is one which outputs cannot be forecast from the initial conditions, along a straight or stable trajectory, i.e., a system which response is not proportional to the stimulus applied, and which allows multiple solutions. This dynamics is the consequence of transitions between order and chaos, which derive from multiple causes of multiple relationships in network, from a continuous interaction between the external and the internal. | Agar, 1999; Bloch, 2005; Bokeno, 2008; Capra, 1983, 1996; Larsen-Freeman , 2012; Long, 2004; Miguelez, 2011; Murray, 1998 |
| Open and dissipative system | A system that absorbs and dissipates energy and matters from the environment, sustaining itself through the continuous flow and exchange of components or energy. | Bertalanffy, 1972; Bloch, 2005; Bousquet & Curtis, 2011; Larsen-Freeman , 2012; Manson, 2001; Prigogine, 1997 |
| Dynamic and irreversible System | Irreversibility is determined by temporal insertion, i.e., any ‘after’ is different from ‘before’, resulting in the impossibility of understanding complex systems by means of their observation in a single moment in time. | Bloch, 2005; Larsen-Freeman, 2012; Prigogine, 1997 |
| Fractal Patterns | The lowest point of the image contains almost all the information of the object represented. Thus, the part is in the whole and the whole is in part, enriching the knowledge of the parties by the entirety and of the entirety by the parties. | Bloch, 2005; Gleick, 1987; Morin, 2010, 2011 |
| Recursion | Generating circuit in which the outcomes and effects are the producers and causers of what they produce, in a self-constituting, self-organizing and self-producing cycle. The system exists at several scales (or recursion levels) and several recursive dimensions, i.e., it belongs to several systems’ chains. | Ashby, 1970; Beer, 1985; Larsen-Freeman, 2012; Morin, 2010, 2011 |
| Retroactivity | Positive or negative feedback, the multiple retroactions of a system are inter-related and suffer the effects of uncertainty. | Miguelez, 2011; Morin, 2010; Rickles, Hawe & Shiell, 2007 |
Table 7: Essential concepts of the complexity theory. Source: organized by the authors.
With the principles considered essential to the theory of complexity defined and gathered, the possibility of understanding complex phenomena can be facilitated from a coherent approach. For this reason, these principles were changed into the format of questions, besides the questions proposed by Agar (1999). The issues and their relationship with the essential concepts, in addition to the authors who approach them, are listed in Table 8.
This approach by means of questions allows the researcher to check whether the phenomenon intended for study presents some aspect that configures it as a complex system and, therefore, complexity is the proper approach to its treatment.
Table 8 - List of analysis questions with the fundamental concepts of complexity. Source: organized by the authors.
In the face of the need for new approaches to the everyday phenomena for which traditional Cartesian thought is inadequate, the theory of complexity seems to be a coherent alternative. Therefore, this article intended to gather, understand and define the basic concepts of this approach, including the concepts of: adaptability; attractors; self-organization; co-evolution; dependence sensitive to initial conditions or chaotic behavior; emergency; dynamic equilibrium; unpredictability; nonlinearity; open and dissipative system; dynamic and irreversible system; fractal patterns; recursion; and retroactivity.
These essential principles were organized as questions which can guide new researchers in the area, avoiding the distortion of concepts and their misuse, especially when concepts are appropriated by different areas, as is common in studies of complexity. These questions are:
These issues represent an approach for the analysis of any phenomenon. It allows checking if the phenomenon presents characteristics that configure it as a complex phenomenon and, therefore, if the theory of complexity is a conceptual basis suitable to its approach.
At this point, it should be emphasized that this research does not propose to discuss issues of epistemological and methodological order. It is not, therefore, a question of producing an approach for dealing with the complexity. This article contributes exposing in a single text the common definitions of the main concepts of the area and where they can be applied, allowing authors less familiar with them, have a starting point to avoid distortions or misappropriations of them, filling a gap of the literature on this kind of topic.
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