Complexity Measures

One of the problems in studying the mechanisms underlying complex systems and phenomena is the lack of a functional definition of complexity. However, there have been several attempts to define the complexity of a given system through a measure of complexity. Without being a definition of complexity, having a numerical scale to compare the complexity of different phenomena is very useful.

Although there are many complexity measures, each of them tends to be context dependent and attempts to provide the generic structure that can provide a useful framework for such measures are still insufficient. Moreover, in many of the complex problems it must be borne in mind that a useful measure of complexity has the objective component – which is a function of the number of elements of the system and their relations – but also a subjective component dependent on the context of the problem. This last component is a function of the distance from the complex system to a reference model or structure to simplify given the purpose for which the measure of complexity is being applied.

As a challenge, each problem will have a “constant” objective complexity and a number of subjective ones. This is particularly important in organizational problems in which multiple stakeholders naturally have a diverse set of reference simplicities, stemming from their view points and perspectives.

Entropy, Control of systems, Chaotic synchronization, NLP algorithms, SVD decomposition, Lyapunov direct method, Logistic map, Rossler attractor, Lorenz attractor, Cohomology