Measuring Complexity of Chaotic Systems With Cybernetics Applications

Complex Systems

A complex system is defined as one in which the individual components that make up the system are by themselves simple but which produces complex behavior due to varied interactions amongst themselves (Northrop, 2010). The study of complex systems has been nascent in the past and has come to prominence only in the last couple of decades. This has been made largely possible by the availability of high-end tools for high speed computation and analysis.

Complex systems possess some basic properties, listed below (Lloyd, 2001).

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  They are composed of simple components.

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  The interactions among components happen in a non-linear fashion.

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  Control of the systems is not centralized.

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  The systems show evolution and learning and adapt to improve themselves.

Some examples of naturally occurring complex systems include brain, immune system and respiratory system to name a few. A healthy human heart is known to produce complex beat-to-beat variations. Brain networks in schizophrenia patients have lower complexity than corresponding networks in a healthy human brain. In the physical world, complex systems are frequently encountered in fields like dynamics, information processing, cryptographic protocols, weather prediction, computation and study of population and evolution. For example, pseudo-random sequences used in secure information storage and transmission systems are designed to have high complexity (to resist malicious attacks). What makes complex systems really interesting is that they exhibit some very interesting behavior, even though the underlying equations may well be simple and deterministic.