Systems and Dynamics: Some Useful Definitions

Some useful definitions when studying the behavior, properties and dynamics of systems (Richard L. Sanders).

Closed System

A closed system is one that is isolated from its environment. This kind of system uses its own internal reserve of potential energy, and as reactions take place, entropy rises irreversibly to a maximum. Thermodynamic equilibrium is reached, and the system can no longer produce work.

Open System

An open system is one in permanent interaction with its environment, with which it exchanges energy, matter and information. Because of the energy flow through the system and the dumping of “used” energy into the environment, its entropy is maintained at a relatively low level. This system is capable of performing work.

Positive Feedback

Positive feedback loops contain the dynamics for change in a system, growth and evolution.


Negative Feedback

Negative feedback loops represent control and stability, the establishment of equilibrium and self-maintenance.


Combination of Positive and Negative Feedback

This is commonly occurring behaviour, rapid growth followed by stabilisation.


The Dynamics of Maintenance and Change

Every system has two fundamental modes of existence and behaviour: maintenance and change. The first, based on negative feedback loops, is characterised by stability. The second, based on positive feedback loops, is characterised by growth (or decline). The coexistence of the two modes is at the heart of any dynamical system.

Homeostasis: Resistance to change

Formally: The ability or tendency of an organism or cell to maintain internal equilibrium by adjusting its physiological processes.

Informally: A homeostatic system (an industrial firm) is an open system that maintains its structure and functions by means of a multiplicity of dynamic steady states rigorously controlled by interdependent regulation mechanisms. Such a system reacts to random changes in the environment to maintain stability.


For a biological system, to endure is not enough; it must adapt itself to time dependent changes in the environment and evolve. Otherwise, outside forces can disorganise and ultimately destroy it. A key to unlocking this apparent paradox can be found in diversity.


The law of requisite variety from Ross Ashby (1956) states that the regulation of a system is efficient when it depends on a system of controls as complex as the system itself. Variety permits a wider range of response to potential forms of aggression. Variety also produces the unexpected, which is the seed of change.


  • Without catalysis: (A + B = AB)
  • With catalysis: (A + B + C = AB + C)

Auto catalysis

  • Catalysis BA: A + B + BA = AB + BA
  • Catalysis AB: A + B + AB = BA + AB


  • Chaos: too much connectivity (random changes can cause avalanches of change; positive feedback)
  • Order: too little connectivity (random changes are damped and system returns quickly to ordered state; negative feedback)
  • Edge of Chaos: right balance between positive and negative feedback leading to adaptation of the network

Two Necessary Conditions for Evolution

  • “Right” level of diversity.
  • “Right” level of connectivity.

Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

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