The dynamics of systems

Copyright 2021 Graham Berrisford. A chapter in the book Updated 25/05/2021 18:05


Reading online? If your screen is wide, shrink the width for easier reading.

This is the fourth chapter in part one of the book.


Systems thinking ideas introduced in the previous chapters are sometimes misinterpreted. Some terms and concepts are misused in discussion of human society. Some distinctions that seem obvious at first sight turn out not be. This chapter helps you avoid confusion by disentangling ideas about dynamics (change, behavior and flows over time). Don’t worry if you don’t get all the ideas first time through. When they reappear in later chapters, you may find it helps to return here.


Dynamical and stable (recap) 1

Structures and behaviors. 1

Persistence and transience. 2

Discrete and continuous dynamics. 3

Systems and processes. 3

Open and closed systems. 4

Physical and logical boundaries. 4

Flows of information and other things. 5

Homeostatic and progressive dynamics. 6

Changing state and changing rules. 6

Remarks. 7


Dynamical and stable (recap)

In cybernetics, system dynamics and soft systems methodology, every system of interest has two contrasting properties. First, it is dynamic in the sense it displays behavior and changes from state to state over time. Structures within the system interact in describable behaviors to change its state and/or produce outputs from inputs. Second, it is stable in the sense its way of behaving is regular enough to be modelled. It is a describable pattern of behavior (however transient) in the ever-unfolding process that is the universe.

Structures and behaviors

Structures are the results (side effects or outputs) of behaviors, and they change over time.


We describe reality in terms of structures (continuants or objects that exist in space, and persist) and behaviors (occurrents or processes that happen over time, and change the state of structures). This dichotomy is so fundamental to our descriptions of reality that we draw the distinction using many words. This table of word pairs is far from exhaustive.


Structural elements

Behavioral elements


















The distinction may seem clear. However, a hierarchy of behavioral activities (a functional decomposition) is usually indistinguishable from a hierarchy of the structural abilities needed to perform those activities (a capability map).


And the chapter on system dynamics discusses how, when a structure/object changes state over time, or a variable changes its value, the succession of state changes can be represented on a graph as a function of time or a line of behavior, as shown in figure 7/1/1 in Ashby’s “Design for a Brain”(1954).



Suppose the state vector has two or three numerical state variables. Its value at any time can be represented as a point on a two or three-dimensional graph, and its trajectory over time can be shown visually as two or three-dimensional shape.

Persistence and transience

What persists over one time span is transient over a longer time.


Persistent means continuing to exist over a given time-span. Transient means bounded in time from start to end. The distinction is related to the structure/behavior one. We usually think of structures in space (like a steam engine, animal, mobile phone, farm or shipyard) as persistent three-dimensional entities. And we think of behaviors as transient.


However, some structures are distributed in space. For example, consider the solar system (solids connected in a network by physical forces) and the members of a social entity (actors connected in a logical network by communication events). Over the long term, both the parts and the whole of those structures have a finite life span.


Behaviors might plausibly be classified into three kinds: persistent (the motion of planet, or an electric current), transient (summers, concerts, weddings and sunrises) and instantaneous (an electrical pulse, switching a light on, a heartbeat). But these distinctions are relative to the time span of interest to us in our “bounded context”. For example, a geologist or a dendrologist may see a summer as a discrete event.


7/3 “If the event [or process] occurs in a system whose changes are appreciable only over some longer time, it may be treated without serious error as if it occurred instantaneously.” Ashby’s “Design for a Brain” (1954)

Discrete and continuous dynamics

Over a long enough time, a process can be seen as an event.


Here, continuous (cf. analogue) means change is smooth and uninterrupted. A system can change state continuously in response to signals that are analogue (vary continuously along a spectrum) or forces that are continuous. Consider the hands of a clock driven by an electric motor. By contrast, discrete (cf. digital) means change occurs in steps over time. Consider the score board of a tennis match, which is driven by the winning of points.


A graph representing a continuous line of behavior is smooth, one that shows discrete state changes is jagged.



The shorter the time steps, the more discrete change steps resemble continuous state change. And to paraphrase Ashby, given a system that takes a long time to change from one state to the next observably different state, a continuous process may be described as a discrete event. Rather than speak clumsily of discrete event dynamic systems (DEDS), we will speak of “event-driven systems”.

Systems and processes

Over its life time, a system can be seen as process.


While at university, I was taught that a system can be described as a structure, a black box, that consumes input(s) and produces output(s). Examples included a farm and a shipyard. Later, by contrast, I was taught that a process is a transient behavior, it runs from start to end, and halts when it delivers a desired result (that is, a state change or output of some value to some other program or a person.)


This distinction is related to the persistent/transient one. However, it turns out that every system is transient; it has a life time; it starts at some point in time and stops at a later point. It may halt for any of the reasons under closed systems below. And a process can be seen as a black box that consumes input and produces output.

Open and closed systems

“Every living organism is essentially an open system.  It maintains itself in a continuous inflow and outflow…” Bertalanffy 1968


An active structure may be seen as an open system, as a black box that consumes inputs and produces outputs. The classic representation of such an open system is a SIPOC diagram.




Open system



à Inputs

à Processes à

Outputs à



By contrast, a closed system runs without input or output, under its own internal drive. For example, using “system dynamics”, a system is modelled as a set of stocks connected in a network by inter-stock flows in feedback loops. The system runs under its own internal drive.




Closed system




Stocks and Flows




However, no closed system is eternal. Over its life time, a closed system transforms an initial state into a final one. Given some initial parameters, such as initial stock levels, it will then proceed to change state over time under its own steam. Sooner or later it will halt, when it exhausts some resource, or reaches a specified time limit or some other terminal condition. While it runs, or at the end of its life, it can output a graph showing the system’s lines of behavior over time.




“Closed” system



à Parameters

à Process à

Graph à



System or process? In this graphic of a closed system, the parameters look like inputs, the closed system looks like a process, and the graph is the desired result.


The chapter on social entity thinking discusses how some system thinkers say the Purpose Of a System Is What It Does (POSIWID), which perversely implies that when a closed system exhausts some stock or resource and stops, that reveals its purpose.


Core concepts: System environment: the world outside the system of interest. Closed system: a system not connected to anything outside its boundary. Open system: a system connected to its wider environment by inputs and outputs. It is characterized by how it responds to inputs (aka events, disturbance or perturbations). Process: a sequence of activities that changes a system’s state and/or transforms inputs into outputs.

Physical and logical boundaries

“The distinction between an external (black-box, abstracting from the contents of the box) and internal (white-box) view is common in systems design. The external view depicts what the system has to do for its environment, while the internal view depicts how it does this.” ArchiMate 3.1.


Physical boundaries are more obvious. We see the skin of a biological organism as its boundary. Sometimes, business architects draw a boundary around an entity located in space, such as a factory or a shipyard. More often, they draw a logical boundary around actors distributed in space and connected by information flows.


System boundaries can be nested. A boiler transforming water into steam may been as a system and/or a subsystem of a steam engine. The human heart can be seen as a system and/or a subsystem of the body. Boundaries can also overlap.


Core concepts: System boundary: a line separating a system from its environment. System interface: a description of inputs and outputs that cross the system boundary, and/or services offered to system users.

Flows of information and other things

“Another development which is closely connected with system theory is that of… communication. The general notion in communication theory is that of information.” Bertalanffy 1968


Flows cross system boundaries. Flows pass between interacting subsystems, actors or stocks within a system. However note that there are at least four kinds of flows that overlap and are entangled.


·       Physical flow: the conveyance of force, matter or energy from one place to another

·       Data flow: the conveyance of information in a message from a sender to a receiver.

·       Causal flow: the progress from a cause to an effect (or actor to what is acted on).

·       Denotic flow: the conveyance of goals, duties or obligations.


Flows of all kinds appear later chapters.


Data/information flows are critical in cybernetics and social entity thinking. Communicating actors exchange messages about phenomena of common interest. Information or meaning is found in the sender’s encoding of a data structure, with reference to a language, and a receiver’s decoding of that data structure, with reference to a language. Clearly, for successful communication, actors must share the same code or language. (Where mistakes cannot be allowed, in science for example, domain specific languages are defined.)


In EA, given that the focus is on information flows rather than material flows, the relationship of a business to the external actors it monitors and serves or directs may be seen as a regulator-to-target feedback loop.


Business activity system

Feedback loop

Business environment


ßstate information



Consumes inputs

Produces outputs

Maintains system state

ß Inputs

à Outputs

External actors

Environment state


Core concepts: Communication: the exchange of information between senders and receivers. Information: a structure or behavior that represents something, phenomenon, decision or direction.

Homeostatic and progressive dynamics

Over its life time, a system may move in and out of stable states.


The systems of interest are dynamic in that they change state over time. A homeostatic entity, by means of a feedback loop, maintains its state variables within an optimal range and might be called static or stable. By contrast, a progressive entity or process continually advances its state variables (e.g. a rocket, or an information system).


It has been said that “any system, left to itself, runs to some equilibrium”. A system may run to a stable state because it empties a resource, or without the input of energy it grows cold, or it dies, or it is drawn towards an attractor state and stays there or thereabouts.


An attractor is a state vector (a set of state variables) with values to which a system is drawn (given various starting conditions). Systems with a state close to an attractor tend to remain close it, even if slightly disturbed. Shown on a graph, an attractor can be a point, a line, a curve, or a multi-dimensional manifold. It can even be a set with a fractal structure - known as a strange attractor.


However, a system may instead stay in one state for a while, become volatile for a while, then be attracted back to the first state or towards another state. As anybody with heart arrhythmia knows, a physical system may behave regularly, then irregularly, then regularly again.

Changing state and changing rules

Between generations, a system mutates, or is changed, into a different system.


The universe may be seen as a continuously unfolding process, in which no entity stands still and everything changes. By definition, an activity system is a pattern of behavior, carved out from that ever-unfolding process. It is a way of behaving that can be described or modelled, using some system definition method, however transient that pattern of behavior may be.


Ashby showed how cybernetics can explain some interesting kinds of behavior observable in animals and machines, both homeostatic behaviors and non-linear behaviors. He modelled the state of such a physical entity in the state variables of an abstract system, which is defined in terms of its way of behaving - how it changes state over time - whether autonomously or in response to external events.


Ashby’s “Design for a brain”

5/7 It must be noted the adaptation is commonly used in two senses, which refer to different processes. The distinction may best be illustrated by the inborn homeostatic mechanisms – the reaction to cold by shivering for instance… [Historically] the first change involved the development of the mechanism itself [by a mutation]; the second change occurs when the mechanism is stimulated into showing its properties [changing the state of an animal].”


Ashby’s “Introduction to Cybernetics"

4/1 It will be seen that the word “change” if applied to such a machine can refer to two very different things. There is the change from state to state, which is the machine’s behaviour, and which occurs under its own internal drive, and there is the change from transformation to transformation, which is a change of its way of behaving, and which occurs at the whim of the experimenter or some other outside factor. The distinction is fundamental and must on no account be slighted.” Ashby’s “Introduction to Cybernetics”


In short, in a dynamic system, the word “change” can refer to a system changing state, or to it changing into a different system. A state change is a discrete change from state to state, in the course of a systems regular way of behaving. By contrast, a mutation is a discrete change that replaces one system or way of behaving by another; it produces a new system version or generation.


This table is an attempt to distinguish further varieties of system change.



State change


Internal condition-driven

1 State change

2 Internal metamorphosis

External input-driven

3 State change

4 Inter-generational evolution

External parameter-driven

5 (Re)start

6 (Re)configuration



1.     The tick tock of a clock. Awake to asleep.

2.     Metamorphosis from egg to adult, or caterpillar to butterfly.

3.     The state change when a free-living organism reacts to a smell, the sting of a nettle, or a blast of cold air. Or a software system reacts to input messages.

4.     Replacing a system by a new version, as in biological evolution by reproduction with modifications, or software development by incremental version changes.

5.     (Re)start or initialization. Setting the hands of a clock to summer time or winter time. Setting the initial stock levels in a system dynamics model.

6.     (Re)configuring a machine from one way of behaving to another. Configuring a clock to run backwards instead of forwards.


Note again that all description is relative to the interest you bring to the subject matter. We may see the metamorphic change from a caterpillar to a butterfly as either a state change or a mutation, depending on the system (the particular state variables and way of behaving) of interest to us. Also in system design, we can design for mutation, make a machine that is configurable, can be switched by some kind of input parameter from realizing one system to another.


The chapter on system change discusses why Ashby and Maturana considered continuous mutation, or a continuously “self-organizing system”, to be a contradiction in terms, and how Ashby’s classical cybernetics defines a mechanism for actors to re-organize a system they play roles in.


If you are missing discussion of other terms (such as emergent properties, holism and reductionism, hierarchies and networks) don’t worry, we’ll get to them later.