Yaneer Bar-Yam, Introduction to the study of complex systems, in Edward Elgar Handbook of Research Methods in Complexity Science (in press).
Complex systems analyses range from detailed studies of specific systems, to studies of the mechanisms by which patterns of collective behaviors arise, to general studies of the principles of description and representation of complex systems. These studies enable us to understand and modify complex systems, design new ones for new capabilities or create contexts in which they self-organize to serve our needs without direct design or specification. The need for applications to biological, cognitive, social, information and other systems is apparent.
For example, biology has followed the approach of accumulating large bodies of information about the parts of biological systems, and looking for interpretations of system behavior in terms of these parts. Yet, it has become increasingly clear that biological systems and their health and disease conditions are better understood as emergent collective behaviors of spatially structured networks, so that dependencies rather than components are the essential property to be understood. The role of information in biological action and the relationships of structure and function are only beginning to be probed by those who are interested in biological systems designed by nature for their functional capabilities. Underlying these systems are a wealth of design principles in areas that include the biochemical networks [1-5], immune systems [6-9] and neural systems [10-12], and animal behaviors such as the swimming mechanisms of fish  and the gaits of animals . These systems and architectures point to patterns of function that have a much higher robustness to failure and error and a higher adaptability than conventional human engineered systems.
Computers have made a transition from systems with tightly controlled inputs and outputs to networks that respond on demand as interactive information systems . This has changed radically the nature of their design. The collective behaviors of these networked computer systems, including the Internet, limit their effectiveness. Whether these have to do with the dynamics of packet loss in internet traffic , or cyberattacks [17-20] that, at times, have incapacitated a large fraction of the internet, these effects are not small. The solution to these problems is understanding collective behaviors and designing computer systems to be effective in environments with complex demands and to have a higher robustness to attack.
The human brain is often considered the paradigmatic complex system. The implications of this recognition are that cognitive function is distributed within the brain and mechanisms may vary from individual to individual. Complete explanations of cognitive function must themselves be highly complex. Major advances in cognitive science are currently slowed by a combination of efforts to explain cognitive function directly from the behavior of individual molecular and cellular components, and on the other hand by aggregating or averaging the cognitive mechanisms of different human beings. Still, diverse advances that are being made are pointing the way to improvements in education , man-machine interfaces [22-24] and retention of capabilities during aging [25-28].
Recent global crises, including the global financial crisis, the global food crisis, social unrest including the Arab Spring, and the Ebola epidemic and other pandemics, have demonstrated that global connectivity leads to vulnerabilities due to the high rate of global travel, and the rapid propagation of economic and social influences [29-35]. Many of the key problems today have to do with “indirect effects” of human activities that may have substantial destructive effects on the human condition. These include global warming and ecological deterioration due to overexploitation of resources. Effective approaches to these problems will require an understanding of both the environmental and socioeconomic implications of both current actions, and of actions that are designed to alleviate these problems . For example, the problem of global warming includes the effects of large scale human activity interacting with both the linear and potentially non-linear climactic responses. Despite the grave risks associated with global warming, a key factor impeding actions to alleviate it are fears of major impacts of such efforts on socioeconomic systems. Better understanding of the potential effects of such interventions should enable considered actions to be taken.
Other diverse social system problems may be linked to increasing societal complexity in healthcare, the education systems and governance more generally. Current approaches continue to be dominated by large scale strategies that are not effective in addressing complex problems. Even with the appearance of more holistic approaches to, e.g. third world development [37-38], the basic concept of existing strategy remains weakly informed by complex systems insights. This gap is an opportunity for major contributions by the field of complex systems, both at the conceptual and technical levels. Further contributions can be made based upon research projects that emphasize the intrinsic complexity of these systems.