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  • Writer's pictureKayleanna Giesinger

Complex Systems

Emergent Behaviour

In a study by Philip Roundy, Mike Bradshaw and Beverly Brockman (2018) the emergence of entrepreneurial ecosystems is examined. An entrepreneurial ecosystem is a social and economic environment that incubates creativity and innovation. Often in these ecosystems’ entrepreneurs have a greater chance for success. The significance of this behaviour, in terms of complex systems, is that the system is a self-organizing complex adaptive system where at a venture level the entrepreneur wouldn’t have the same access to support and resources. Likewise, in terms of emergence, when analysing a single venture, you wouldn’t be able to anticipate a network of ventures forming an ecosystem. It is stated clearly that the innovation within these ecosystems both influence and are the result of emergence.

The fine scale units of this emergence are determined to be of three main areas. The first is intentionality and adaptive tensions of the entrepreneurs. This is observed through support and interactions between the individual entrepreneurs. Then, there is coherence of the entrepreneurial activities seen through the direction and framework of the collective venture developments. Lastly is the injections of resources into the ecosystem as a result of the agents providing for each other. The nature of these interactions are a result of individual (agents), organizational and socio-cultural forces. The result is creation of innovative organizations that produce products and initiatives that generate value for society.

The degree to which the behaviour cannot be anticipated is hard to determine. Often successful businesses are hard to pinpoint at a start-up level. Therefore, considering the emergence of entrepreneurial ecosystems in this complex system only adds a level of uncertainty in the mathematical predictions. The paper suggests using agent-based models to better understand this system. While agent-based models are useful in simulating systems that are nearly impossible to analytically assess, they have their own levels of unreliability. Often these models trivialize human behaviour and are self-fulfilling prophecies. If a model indicates a match it doesn’t always mean that it generates meaningful data and predictions. With enough data the model can anticipate behaviour, but this information should be used with caution.


Resilience, at its core, can be defined as the persistence of system relationships which enable it to recover from disturbances (Deffuant & Gilbert, 2011). Depending on the system this definition can be interpreted in a variety of ways. Table 7 summarizes the various forms and interpretations of resilience. 

The main mathematical mechanisms of resilience can be broken into two areas. The first mechanism for mathematical interpretation is using eigenvalues. This method isn’t as robust or precise in quantifying resilience. However, it reveals system behavior and can indicate the system resilience at a basic level. To quantify resilience this way, the eigenvalue is the indicator of resilience. The least negative eigenvalue (slowest mode) is what limits the speed that the system can recover from a disturbance and the faster the return to the stable fixed point, the larger the resilience (Fieguth, 2017). 

The second mechanism is through interpreting the system basins. Figure 7 visually represents system basins.

Figure 7: System basins of attraction. Each regime is an ‘alternative state’ and both are resilient to stay within their own basin (Fieguth, 2017).

Figure 7 shows a two-dimensional non-linear dynamic system where its behavior corresponds to two basins. Each regime is an ‘alternative state’ with its own corresponding behavior and resilience. Therefore, if a system is perturbed into a different basin a catastrophic state transition can occur and the shift is irreversible. This means that the distance to the nearest unstable fixed point isn’t what matters. It is the distance to the basin boundary that is important. This magnitude and the speed that the system settles back into its basin is the corresponding resilience.

Considering everything discussed already, there are certain challenges when formulating a definition for system resilience. Table 8 summarizes these challenges.

Natural and human systems

Natural and human systems are dynamic and seemingly unpredictable at times. Development of these systems can cause gradual global changes that can come in many forms (Scheffer M. , 2009). When subject to continual perturbations systems can become weakened and result in spontaneous catastrophic changes. Mathematics and research have allowed for certain understanding of these complex systems. Specifically, the nature of their evolution and the prediction of the approach to catastrophic states.

Gradual state and parameter changes are always happening in all systems. In societal systems, this gradual change can be perceived as progress. In natural systems it can be called evolution. As certain perturbations take place these complex systems can slowly lose resilience until even a minor perturbation can push them over a tipping point (Scheffer M. , 2009). Even systems that originally appeared Uni-Stable can progress to a point of Bi-Stability and result in a hysteresis or irreversibility. Graphically this is demonstrated in Figure 7.

Figure 7: Systems are subject to many natural perturbations that can cause them to shift and become bi-stable (Fieguth, 2017)

These radical changes might be rare, but they are very important and impactful to society (Scheffer M. , 2009). In the book A Short History of Progress by Robert Wright, he discusses the rise and fall of societies and the gradual progress that is taken before a catastrophic fall. It is stated that, “Many of the great ruins that grace the deserts and jungles of the earth are monuments to progress traps, the headstones of civilizations which fell victim to their own success” (Wright, 2004). He explains that the solutions often produced to fix the problems created by our own progress are created by further progress. Which pushes us further along the path to the tipping point. An example of this is the dying of the coral reefs. For the longest time, reefs were studied as a system of resilient nature, able to adapt to many pollutants and challenges it faced. However, a dramatic shift occurred when a species-specific pathogen caused “mass mortality” to the sea urchin (Scheffer M. , 2009). Now coral reefs are dying out rapidly because this final perturbation pushed it over the edge after human impacts weakened its state. It is suggested that the key to explaining collapses isn’t necessarily the external forces though, but the “gradually increasing fragility of these elaborate” systems (Scheffer M. , 2009).

These catastrophic shifts can be explained by a few phenomenon. A bifurcation corresponds to an abrupt or discontinuous change in a system as a parameter is changed. Building off that hysteresis occurs after a bifurcation that causes the system to resists reversibility. This is demonstrated in Figure 8.

Figure 8: A hysteresis loop, where a bifurcation occurs, the system drops off its current stable state and isn’t easily reversed back to its original state (Fieguth, 2017).

Luckily, there are warning signs when approaching the tipping point of a system. The most important cue is called “critical slowing down” (Scheffer, et al., 2009). This is the phenomenon where, at a fold bifurcation, as the system approaches the bifurcation its recovery to perturbation slows down. The slowing down often begins far away from the bifurcation point and thus can be used as an early warning system for hysteresis. This is something that has been observed consistently, Wright (2004) mentions that, “While the facts of each case differ, the patterns through time are alarmingly – and encouragingly – similar.” He continues that we should be concerned about the predictability of our mistakes, but also encouraged, “that very fact makes them useful for understanding what we face today.” This means that scientists can observe the small natural perturbations and use the recovery of the system as an indicator of how close a system is to a bifurcation point (Scheffer, et al., 2009). The Precautionary Principal (Fieguth, 2017) integrates well, by being a tool of analysis to compare the costs of a bifurcation to the costs of current system modification. This allows for a quantifiable approach to assign value to making necessary changes to our own global system to ensure conservation for the future.


Current Gross Domestic Product (GDP) calculations doesn’t assign a value to natural resources and lacks the recognition of resource loss. This is because GDP only measures output produced and sold in legal markets. The US Bureau of Economic Analysis describes the GDP as a way of measuring, “how fast is the economy growing,” “what is the pattern of spending on goods and services,” “what percent of the increase in production is due to inflation,” and “how much of the income produced is being used for consumption as opposed to investment or savings”. This means that, “Although GDP and its related concepts are useful in measuring a country’s output, income, and standard of living, they are not perfect measures of quality of life.” (Buck, 2008). Quality of life includes, leisure, environment and human health. For example, a country could increase its current GDP if the regulations on pollution were more lenient, but then the people living in the area could have more health problems and less outdoor spaces to enjoy (Buck, 2008). Likewise, some environmentalists suggest that GDP encourages short term growth at the “expense of long-term global health” (Schapiro, 2017). 

Western policy has been the limiting factor to assigning value to natural resources and pollution. The main issue being that GDP is being misused to indicate things that are not included in the measurements (Costanza, Hart, Posner, & Talberth, 2009). This all started in the United States of America (USA) in the 1930s and 1940s. GDP was used to justify adjusting policies and budgets in such a way to bring the USA out of the depression. Then came the second world war, and the same GDP estimates were used to show that the economy would be fine even though they were providing supplies for the military. The idea of incorporating GDP estimates into the governing structures of all countries was to provide an, “equal voice to all member countries”. Instead, since the USA economy dominated globally, using GDP became more of a global standard that other countries were compared (Costanza, Hart, Posner, & Talberth, 2009). 

Based on this history, the reason for GDP not considering natural resources and pollution is because it was never intended to. Additionally, since the GDP often project values desirable for economic growth, companies continue to use it to push their own agenda. Many decision makers view the GDP as an overall representation of progress (Costanza, Hart, Posner, & Talberth, 2009). Troublingly, one report by the World Bank states that using right rates of GDP growth can solve poverty in the world (Commission on Growth and Development, 2008).


  • Fieguth, P. (2017). An Introduction to Complex Systems. Springer International Publishing,.

  • Scheffer, M. (2009). Critical Transitions in Nature and Society. Princeton University Press.

  • Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V., . . . Sugihara, G. (2009, September 3). Early-warning signals for critical transitions. Nature, 461, 53-59.

  • Wright, R. (2004). A Short History of Progress. Toronto: House of Anansi Press Inc.

  • ​Roundy, P. T., Bradshaw, M., & Brockman, B. K. (2018). The emergence of entrepreneurial ecosystems: A complex adaptive systems approach. Journal of Business Research, 1-10.

  • ​Deffuant, G., & Gilbert, N. (2011). Viability and Resilience of Complex Systems. Berlin Heidelberg: Springer.

  • ​Buck, J. (2008, August 24). Limitations of Using GDP as a Measure of Quality of Life. Retrieved from Economic Perspectives:

  • Commission on Growth and Development. (2008). The Growth Report: Strategies for Sustained Growth and Inclusive Development. Washington, DC: World Bank.

  • Costanza, R., Hart, M., Posner, S., & Talberth, J. (2009, January). Beyond GDP: The Need for New Measures of Progress. Retrieved from Boston University:

  • Schapiro, K. (2017, February 23). Why GDP Is Not an Accurate Measure of the Economy. Retrieved from Investopedia:

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