Purpose and description
A theory in mathematics and geometry to study how small changes in parameters of a non-linear system can lead to sudden and large changes in behavior of a system.
Poston & Stewart 
Historically used as a synonym for systems theory, it is a field of study of the communication and control of regulatory feedback in both living and non-living systems (e.g., organizations, machines).
A field of study in mathematics with applications in a wide number of disciplines to explain a dynamic system and that is highly sensitive to the initial conditions, so that small changes in initial conditions produce wildly different results. The changes occur through fixed rules about changing relationships, and without randomness.
General systems theory
Less of a theory than a way of finding a general theory to explain systems in all fields of science. It was not intended to be a single theory of systems, but more of a systematic inquiry into different domains of philosophy, science, and technology.
van Bertalanffy 
Learning organizations theory
A description of organizations that facilitate learning by its members and continuously transforms itself. Systems thinking approaches are the conceptual basis for understanding the organization in its environment, and provides a basis for other key characteristics, namely a process of learning (personal mastery), the challenging and building of mental models, and the development of a shared vision and team learning.
Path dependency theories
Occurs in economics, social sciences, and physics, and refers to the explanations for why processes can have similar starting points yet lead to different outcomes, even if they follow the same rules, and outcomes are sensitive not only to initial conditions, but also to bifurcations and choices made along the way.
Punctuated equilibrium (in social theory)
Theory inspired from evolutionary biology  to explain long periods of stasis interrupted by rapid and radical change, particularly as applied to the evolution of policy change or conflict.
Baumgartner & Jones 
Agent-based modeling (ABM)
ABMs are used to create a virtual representation of a complex system, modeling individual agents who interact with each other and the environment. Although the interactions are based on simple, pre-defined rules, in a complex system these simulations allow for the identification of emergence and self-organization.
Network Analysis (or Social Network Analysis)
Network analysis uses graphical methods to demonstrate relations between objects. Grounded in computer science, it has applications in social, biological, and physical sciences. Social network analysis involves application of network theory to social entities (e.g., people, groups, organizations), demonstrating nodes (individual actors within a network), and ties (the type of relationships) between the actors, and uses a range of tools for displaying the networks and analyzing the nature of the relationships.
This is a strategic planning method that uses a series of tools to identify and analyze possible future events and alternative possible outcomes. These can involve quantitative projections and/or qualitative judgments about alternatives. The value lies more in learning from the planning process than the actual plans or scenarios.
Systems dynamics modeling
Not a single method, but an approach that uses a set of tools to understand the behavior of complex systems over time. The methods focus on the concepts of stocks and flows and feedback loops. They are designed to solve the problem of simultaneity (mutual causation) by being able to change variables over small periods of time while allowing for feedback and various interactions and delays. The common tools include causal loop diagrams and stock and flow diagrams.
Causal loop diagrams (CLDs)
CLDs are a system dynamics tool that produces qualitative illustrations of mental models, focused on highlighting causality and feedback loops. Feedback loops can be either reinforcing or balancing, and CLDs can help to explain the role of such loops within a given system. CLDs are often developed in a participatory approach. The drawings can be further developed by categorizing the types of variables and quantifying the relationships between variables to form a stock and flow diagram.
Williams & Hummelbrunner 
Innovation (or change management) history
Innovation or change management history aims to generate knowledge about a system by compiling a systematic history of key events, intended and unintended outcomes, and measures taken to address emergent issues. It involves in-depth interviews with as many key stakeholders as possible to build an understanding of the performance of the system from a number of different points of view.
Douthwaite & Ashby 
Participatory Impact Pathways Analysis (PIPA)
PIPA is a workshop-based approach that combines impact pathway logic models and network mapping through a process involving stakeholder engagement. PIPA workshops aim to help participants to make their assumptions and underlying mental models about how projects run explicit and to reach consensus on how to achieve impact.
A set of tools, such as flow charts, to provide a pictorial representation of a sequence of actions and responses. Their use can be quite flexible, such as to make clear current processes, as a basis for identifying bottlenecks or inefficient steps, or to produce an ideal map of how they would like them to be.
Stock and flow diagrams
Stock and flow diagrams are quantitative system dynamics tools used for illustrating a system that can be used for model-based policy analysis in a simulated, dynamic environment. Stock and flow diagrams explicitly incorporate feedback to understand complex system behavior and capture non-linear dynamics.
Systems archetypes are a number of generic structures that describe common behaviors between the parts of a system. They provide templates to demonstrate different types of balancing and reinforcing feedback loops, which can be used by teams to come to a diagnosis about how a system is working, and particularly about how performance changes over time.