Chaos can be accurately defined:

• Chaos deals with deterministic systems whose trajectories diverge exponentially over time
• Informally, Chaos is also used to refer to disorder and randomness

Thus, Chaos is concerned with minimum parameters and the dynamics of their values, while the study of complex systems is concerned with both the structure and the dynamics of systems and their interaction with their environment.

Systems Theory investigates both the principles common to all complex entities, and the (usually mathematical) models which can be used to describe (analyze) them.

Systems theory was proposed in the 1940's by the biologist Ludwig von Bertalanffy

• He emphasized that real systems are open to, and interact with their environments
• Can acquire qualitatively new properties through emergence, resulting in continual evolution
• Focus on the arrangement of / relations between parts which binds them into a whole

Holism - a view that an entire system of beliefs must be analyzed rather than simply its individual components

Systems analysis (P- Metrx analysis approach ) applies to principles for controlling (usually socio-technical) systems.

• Analyzing multiple objectives, constraints and resources

• A system that behaves in a straightforward, mechanical and predictable manner, e.g. the balls on a billiard table, a toaster, water pump, etc.
• A Simple System's behavior can be accurately predicated and controlled due to the interaction of a limited number of variables

• A system composed of many interacting (yet inert) parts that can be studied using probabilistic models and statistical methods
• The operating assumption is that its behavior as a whole can be entirely understood by reducing it to its parts-this theory does not consider emergent possibilities

• A complex system arises through the dynamic, non-linear interaction of its component parts, yet embodies emergent possibilities exceeding the sum of those parts
• Examples of complex systems include living cells, the human brain, languages, cities, ecosystems and management organizations which are self-determining

Subtle differences between Complicated and Complex Systems:

• Complicated literally means "Folded Together" (from Latin: cum+plicare)
• a Complicated System is a collection of elements, the resulting behavior is the cumulative sum of the individual behaviors
• Complex (from Latin: cum+plexere) means "Woven Together"
• a Complex System is a collection of elements with a strong interdependence, its cumulative sum is determined by its network structure

Characteristics of a Complex System:

• Presence of many elements (organs, individuals, agents, sub-organizations, etc.)
• Non-linear interactions among elements
• Network structure
• Presence of negative and positive feedback
• Capacity to evolve
• Robustness
• Presence of self-organization phenomena
• Hierarchical structure

Basic Definition:
   Complex Systems Theory includes the study of interactions of the many parts of the system.

• With the analysis of development farther and farther down the sequence of developmental stages, it becomes more and more difficult to predict what will develop based only upon knowledge of the first stage, even when that knowledge is extensive
• Thus even though there is logical development from stage to stage, there is an increasing inability to predict what will actually be the next development milestone. This uncertainty of predictability is called "Chaos"

   Tiny changes in a condition can eventually lead to a huge number of different possible results.

When change occurs in Complex Systems, it occurs in a non-linear fashion:

• Linear change is where there is a sequence of events that affect each other in order as they occur
• In non-linear change, elements are changed by previous elements, but then in turn these changed elements affect elements prior in the sequence
• In non-linear analysis, researchers look at how everything in the sequence has the possibility of affecting everything else in the sequence before and after it - P-Metrx
• Such unpredictable results are called emergent properties, showing how emergent properties facilitate creativity in complex systems
• Emergent properties are still a logical result, just not a predictable one, demonstrating the propensity of systems to be driven away from its equilibrium

The concept of Emergence is extremely relevant in an administrative environment. This is seen not just in the behavior of management, but all those affected by their decisions, Emergence is:

• what parts of a system do together that they would not do by themselves: (collective behavior)
• what a system does by virtue of its relationship to its environment that it would not do by itself: e.g. its function
• In the extreme, it is about how macroscopic behavior arises from microscopic behavior

Reductionism is an approach to building descriptions of systems out of the descriptions of the subsystems that a system is composed of, and ignoring the relationships between them.

• This is a common mistake in most Strategic, Improvement and Performance Planning model

A basic concept in the Systems Approach is that all systems interact with their environment. A premise is that once a system is identified, (boundaries articulated) one may describe:

• The properties of the system
• The properties of the universe (excluding the system) which affects the system, and
• The interactions / relationships between them

When describing a system in the context of its environment, we speak about it’s "Response" and "Behavior"   

• The Response of a system is how it changes when the environment changes in a particular way
• The more general description of a system in the context of diverse conditions is its Behavior
• The concepts of Adaptation and Evolution are directly related to the way a system, or a collection of similar systems, respond and change in the context of their environment

 A network is a description of the connections that allow interactions and influences between parts of a complex system, networks include:

• Transportation networks - roads, thoroughfares, automotive, etc.
• Communication networks - telephone, computer, bulletins, meetings, conferences, etc.
• Utility networks - electric power, HVAC, lighting, etc.
• Supply networks - operational supplies, delivery systems, etc.
• Social networks - employees, faculty, management, community, students, parents, suppliers, customers, etc.

   An important property of the network is its topology: e.g.

• Which elements within an organization are directly connected and the form on network structure
• Each connection of the network can be characterized by properties such as its strength of influence, capacity, etc.

A simple type of pattern is a repeating structure in space;

• The relationship between two types of emergent properties:
• Emergent properties that arise from relationships between parts of a system, and
• Emergent properties that arise from relationships between a system and its environment

The concept of linear relationships suggests that two quantities are proportional to each other:

• Doubling one causes the other to double as well

   Linear relationships are often the first approximation used to describe any relationship

• For example, a linear relationship between the height and weight of a person is different than a linear relationship between the volume and weight of a person

   Feedback is a circular process of influence where action has effect on the actor

• For example, a thermostat that controls the temperature in a house uses feedback. It contains a controller that turns the furnace on and off which heats the room. The thermostat also measures the temperature in the room to determine when to turn the furnace on or off
• The control of the furnace changes the temperature in the room, which is measured by the thermostat that controls the temperature. The goal is a uniform temperature which is specified by the position of the temperature dial - Scientific Analysis

 A powerful way of probing the behavior of a complex system is observing how it responds to a force applied to it, especially the "indirect" effects that occur at different places or at times other than when the force was applied. This is a way of probing the direct/indirect relationships of cause and effect.

• Indirect-in-Space means that the system transfers the effect from the place where the force is applied to other places
• Indirect-in-Time means the system shows different effects later than when the force is applied. Ultimately, if we want to influence the system to change its behavior, knowing the dynamic response of the system is essential - Scientific Analysis